U.S. patent number 10,380,986 [Application Number 16/139,027] was granted by the patent office on 2019-08-13 for means and methods for switching odd and even numbers of matched pickups to produce all humbucking tones.
The grantee listed for this patent is Donald L Baker. Invention is credited to Donald L Baker.
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United States Patent |
10,380,986 |
Baker |
August 13, 2019 |
Means and methods for switching odd and even numbers of matched
pickups to produce all humbucking tones
Abstract
This invention discloses a switching system for any odd or even
number of two or more matched vibrations sensors, such that all
possible circuits of such sensors that can be produced by the
system are humbucking, rejecting external interferences signals.
The sensors must be matched, especially with respect to response to
external hum and internal impedance, and be capable of being made
or arranged so that the responses of individual sensors to
vibration can be inverted, compared to another matched sensor,
placed in the same physical position, while the interference signal
is not. Such that for 2, 3, 4, 5, 6, 7 and 8 sensors, there exist
1, 6, 25, 90, 301, 966 and 3025 unique humbucking circuits,
respectively, with signal outputs that can be either single-ended
or differential. Embodiments of switching systems include
electro-mechanical switches, programmable switches, solid-state
digital-analog switches, and micro-controller driven solid state
switches using time-series to spectral-series transforms to pick
the order of tones from bright to warm and back.
Inventors: |
Baker; Donald L (Tulsa,
OK) |
Applicant: |
Name |
City |
State |
Country |
Type |
Baker; Donald L |
Tulsa |
OK |
US |
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Family
ID: |
65360692 |
Appl.
No.: |
16/139,027 |
Filed: |
September 22, 2018 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20190057678 A1 |
Feb 21, 2019 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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15917389 |
Jul 14, 2018 |
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15616396 |
Jun 7, 2017 |
10217450 |
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14338373 |
Jul 23, 2014 |
9401134 |
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62711519 |
Jul 28, 2018 |
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62569563 |
Oct 8, 2017 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G10H
3/182 (20130101); G10H 1/342 (20130101); G10H
1/18 (20130101); G10H 3/22 (20130101); G10H
1/06 (20130101); G10H 3/186 (20130101); G10H
3/185 (20130101); G10H 3/188 (20130101); G10H
3/181 (20130101); G10H 1/46 (20130101); G10H
2250/235 (20130101); G10H 2220/505 (20130101) |
Current International
Class: |
G10H
3/18 (20060101); G10H 1/34 (20060101); G10H
3/22 (20060101); G10H 1/46 (20060101); G10H
1/18 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
French, Richard Mark, Engineering the Guitar, Theory and Practice,
2009, Springer, New York, USA. cited by applicant.
|
Primary Examiner: Fletcher; Marlon T
Parent Case Text
This application claims the precedence in elements of U.S.
Provisional Patent Application No. 62/711,519, filed 2018 Jul. 28,
U.S. Non-Provisional patent application Ser. No. 15/917,389, filed
2018 Jul. 14, U.S. Provisional Patent Application No. 62/569,563,
filed 2017 Oct. 8, U.S. Non-Provisional patent application Ser. No.
15/616,396, filed 2017 Jun. 7, and U.S. Pat. No. 9,401,134B2, filed
2014 Jul. 23, granted 2016 Jul. 26, by this inventor, Donald L.
Baker dba android originals LC, Tulsa Okla. USA
Claims
I claim the following, and as a Pro Se inventor with limited
resources request the help of the Patent Examiner to state these
claims correctly:
1. A sensor switching system, comprised of: a. two or more matched
vibration sensors, with two or more terminals, matched to produce:
i. the same signal outputs to the same inputs of external
interference, and ii. the same signal outputs to the same inputs of
vibration, with one of two polarities, such that said vibration
signal can be made or arranged to present either normal or opposite
polarity, with respect to another of said matched sensors when
placed in the same physical position, and b. a common connection
point, to which all of all of said sensors are connected by their
terminals which have the same phase of external interference
signal, and c. a switching system, which i. connects at least one
of said sensors to a high output terminal, and ii. connects at
least one of another of said sensors to a low output terminal, and
iii. connects the system reference ground to either said common
connection point or said low output terminal, but not both in
normal operation, except for special cases of circuit testing.
2. The sensors and system as cited in claim 1, wherein the
switching is done by an electromechanical switch, in which two or
more poles connect to the terminals of said sensors, which
terminals are not connected to the common connection point.
3. The electromechanical switching system as cited in claim 2,
wherein one or more of said switch poles not connected to said
sensors are connected to components used for passively modifying
the output signal of said switching system.
4. The electromechanical switching system as cited in claim 2,
wherein the high and low outputs of the system are connected to
electronic circuits intended to modify the system signal.
5. The electromechanical switching system as cited in claim 2,
wherein the high and low outputs of the system are connected to
electronic circuits intended to modify the system output signal,
and one or more of said switch poles are used to select components
used in said electronic circuits to modify said signal.
6. The electromagnetic switching system as cited in claim 2,
wherein the connections of said switching system are made on a
separate, replaceable plug board, such that, a. said board connects
to a plug mounted near to said switching system, with said plug
connected to the switch throws of said switching system, and none
or more poles of said switching system, and b. connections from
each of the throws of said switching system are connected either to
the high or the low outputs of the output of said switching system,
so as to create desired sensor circuits in the order of said
throws, and c. components intended for modification of said
switching system output signal are mounted and selected by one or
more of said poles and throws of said switching system, and d. the
resulting of said switched sensor circuits and their associated
modifying components are presented to the plug area of the board,
to be connected back into the switching system for further
modification and output.
7. The plug board as cited in claim 6, which is programmable by
manually changable interconnects from said throws of said switching
system to said switching system high and low outputs.
8. The sensors and switching system as cited in claim 1, where the
connections are made by solid-state analog switches with digital
control lines to set the state of said switches, said switches
performing the functions of: a. connecting a terminal of one of
said sensors, not connected to said common connection point to
either of: i. nothing, or ii. said high output of said switching
system, or iii. said low output of said switching system, or iv.
said common connection point of said switching system, and b.
connecting said system ground to either of: i. said common
connection point, or ii. said low output terminal, and c.
connecting said common connection point to said low output terminal
for test purposes, and d. connecting passive components within said
switching system to modify the signal output of said system.
9. The sensors and solid-state switching system as cited in claim
8, wherein said digital control lines are driven by a digital
sequencer controlled by an up-down switch, said switch and
sequencer moving the state of the control lines from one sensor
circuit to the next and back, said sequencer acting as a digital
up-down ripple counter with outputs isolated from undesired control
lines by diode or transistor isolation, such that only one desired
sensor circuit and set of signal modification components are chosen
for each output state of the sequencer.
10. The sensors and solid-state switching system as cited in claim
8, wherein said digital control lines are driven by a programmable
micro-controller system, said micro-controller system performing
the functions of: a. driving said digital controls of said
solid-state analog switches according to a program to produce a
desired sequence of possible circuits of said sensors, and b.
driving a set of one or more controls and one or more displays, so
as to allow a user to: i. choose the current sensor circuit and
operating state of said sensor and switching system, and ii. choose
the order of selection of said sensor circuits and operating states
of said system, and iii. inspect said order of selection of said
sensor circuits, and iv. inspect said order of said operating
states of said system, and v. see which of said sensor circuits and
operating states are currently active, and vi. perform testing and
calibration so as to determine the desirability of said order of
said sensor circuits and operating states of said system, and c.
using an analog-to-digital converter to digitize samples of said
output signal of said switching system, and storing said samples,
such that spectral analysis of said output signal can be performed
by said micro-controller using a math processing unit, and d.
performing and storing inverse spectral analysis with a math
processing unit so as to provide analog signals with a
digital-to-analog converter to help the user in ordering said
sensor circuits, according to tone, and e. using said spectral
analysis to determine and adjust the gain of analog output circuits
for said switching system, so that the signals from different said
sensor circuits sound substantially at the same output level.
11. A method for ordering the tones of vibration signals from two
or more sensor circuits, comprised of: a. picking a standardized
way of exciting vibrations, including: i. causing one or more of
the strings of a stringed instrument to vibrate, and ii. playing
one or more notes on a wind instrument, and iii. striking one or
more places on a percussion instrument, and iv. using ultrasonic
excitation on an arrangement of matter, and v. using explosive
excitation on an arrangement of matter, and vi. using
electromagnetic excitation on an arrangement of matter, and b.
measuring and recording said excited vibrations for each and every
available sensor circuit, and c. calculating and storing a complex
frequency spectrum, including magnitude and phase or real and
imaginary parts, from each of said recordings, i. using one or more
orthogonal functions in said calculation, including: 1. sine and
cosine, and 2. Walsh functions, and 3. Chebeshev polynomial
functions, and 4. Haar functions, and 5. Rademacher functions, and
6. Block pulse functions, and 7. Slant functions, and 8. Piecewise
orthogonal functions, and 9. Orthogonal polynomials, and 10.
Legendre polynomials, and d. Calculating inverse transforms of
spectra and storing them as vibration time series samples to aid in
later user identification of tones with said sensor circuits, and
e. adjusting said calculated frequency spectra according to human
psychoacoustics, including: i. A-weighting, and ii. masking
functions, and iii. no adjustments, and f. calculating from said
frequency spectra: i. their relative signal magnitudes, and ii.
their mean frequency, and iii. their individual moments about the
mean, and iv. the roots of said moments about the mean to match
units with mean frequency, and g. weighting said mean and moments
and root-moments into a one or more terms of measure of tone for
each sensor circuit, and h. using said measures, measurements and
calculations to: i. order the selection sequence of said sensor
circuits in a switching system sequence according to measure of
tone, and ii. use relative amplitudes of each sensor circuit
outputs to adjust the amplification of said sensor circuit outputs
to substantially equal loudness, as perceived by the human ear,
and, i. using said measures, measurements and calculations to: i.
calculate the extreme spread of said sensor circuit tones measures,
and ii. match said extreme spread of tonal measures to the
available number of switching states for said sensor circuits, such
that for j number of said switching states, the ration, r,
multiplied j-1 times the lowest tonal measure in said extreme
spread will equal the highest tonal measure in said extreme spread,
and iii. calculate the desired tonal separation of said switching
states as a factor of r times a lower tonal measure to the next
higher one, and j. pick the switching sequence of said sensor
circuits, such that i. the number of said sensor circuits used
matches the number of available switching states, and ii. the tonal
measure of said sensor circuits matches said calculated tonal
sequence according to the ratio, r, as closely and practicably as
possible, iii. except that exceptions may be made to take advantage
of said sensor circuits with larger relative amplitudes, and tones
that may be considered more advantageous, and k. external
communications, for the purposes of: i. testing, and ii.
reprogramming, and iii. control of the switching system with
external computer, display and keyboard equipment, and iv. other
useful functions.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is related to the use of matched single-coil
electromagnetic pickups, as related in U.S. Pat. No. 9,401,134B2,
filed 2014 Jul. 23, granted 2016 Jul. 26, in U.S. NP patent
application Ser. No. 15/616,396, filed 2017 Jun. 7, in U.S.
Provisional Patent Application No. 62/522,487, filed 2017 Jun. 20,
in U.S. Provisional Patent Application No. 62/569,563, filed 2017
Oct. 8, in U.S. Provisional Patent Application No. 62/711,519,
filed 2018 Jul. 28, and in U.S. NP patent application Ser. No.
15/917,389, 2018 (exact filing date subject to granting of
petition) by this inventor, Donald L. Baker dba android originals
LC, Tulsa Okla. USA.
COPYRIGHT AUTHORIZATION
Other than for confidential and/or necessary use inside the Patent
and Trademark Office, this authorization is denied until the
Non-provisional Patent Application is published (pending any
request for delay of publication), at which time it may be taken to
state:
The entirety of this application, specification, claims, abstract,
drawings, tables, formulae etc., is protected by copyright:
.COPYRGT. 2018 Donald L. Baker dba android originals LLC. The
(copyright or mask work) owner has no objection to the facsimile
reproduction by anyone of the patent document or the patent
disclosure, as it appears in the Patent and Trademark Office patent
file or records, but otherwise reserves all (copyright or mask
work) rights whatsoever.
APPLICATION PUBLICATION DELAY
This requests that this NPPA not be published prior to the granting
of the patent.
DESCRIPTION
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not Applicable
NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT
Not Applicable
INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC
OR AS A TEXT FILE VIA THE OFFICE ELECTRONIC FILING SYSTEM
(EFS-WEB)
Not Applicable
STATEMENTS REGARDING PRIOR DISCLOSURES BY THE INVENTOR OR A JOINT
INVENTOR
Not Applicable
TECHNICAL FIELD
This invention primarily describes humbucking circuits for odd
numbers of matched electro-magnetic string vibration pickups, as
used in guitars and basses, also applicable to other musical
instruments with ferrous strings, in which each pickup responds
equally to external electromagnetic fields, otherwise known a hum;
it can also apply to other types of vibration sensors, placed in
other manners on other types of equipment which sensors exhibit
substantially similar bipolar response to desired and detected
signal and to unwanted external electric or magnetic
interference.
BACKGROUND AND PRIOR ART
Single-Coil Pickups
Early electromagnetic pickups, such as U.S. Pat. No. 1,915,858
(Miessner, 1933) could have any number of coils, or one coil, as in
U.S. Pat. No. 2,455,575 (Fender & Kaufmann, 1948). The first
modern and lasting single-coil pickup design, with a pole for each
string surrounded by a single coil, seems to be U.S. Pat. No.
2,557,754 (Morrison, 1951), followed by U.S. Pat. No. 2,968,204
(Fender, 1961). This has been followed by many improvements and
variations. In all those designs, starting with Morrison's, the
magnetic pole presented to the strings is fixed.
Dual-Coil Humbuckers
Dual-coil humbucking pickups generally have coils of equal matched
turns around magnetic pole pieces presenting opposite magnetic
polarities towards the strings. Lesti, U.S. Pat. No. 2,026,841,
1936, perhaps the first humbucking pickup, had multiple poles, each
with a separate coil. Lover, U.S. Pat. No. 2,896,491, 1959, had a
single magnet providing the fields for two sets of poles, one for
each string, with a coil around each set, the pickup design which
most modern humbuckers use. These have been followed by a great
many improvements and variations, including: Fender, U.S. Pat. No.
2,976,755, 1961; Stich, U.S. Pat. No. 3,916,751, 1975; Blucher,
U.S. Pat. No. 4,501,185, 1985; and Knapp, U.S. Pat. No. 5,292,998,
1994;
Humbucking Pairs
Nunan, U.S. Pat. No. 4,379,421, 1983, patented a reversible pickup
that could present either pole to the strings. But the patent only
mentions rotating the middle pickup of three to produce two
humbucking pairs with the neck and bridge pickups, using a 5-way
switching system. It does not present a humbucking pair made with
the neck and bridge pickups. Fender, U.S. Pat. No. 4,581,975, 1986,
may be the first to use the term "humbucking pairs" (column 2, line
31), stating in column 2, line 19, "Thus, it is common for
electrical musical instruments to have two, four or six pick-ups."
Yet, in the 3-coil arrangement of his patent, with the middle
pickup presenting North poles to the strings and the neck and
bridge pickups presenting South poles to the strings, he did not
combine the signals from those pickups to form humbucking pairs.
Instead, he added dummy pickups between them, underneath the pick
guard (FIG. 2), without magnetic poles, for provide the hum signals
for cancellation.
Commonly manufacture of single-coil pickups are not necessarily
matched. Different numbers of turns, different sizes of wires, and
different sizes and types of poles and magnets produce differences
in both the hum signal and in the relative phases of string
signals. On one 3-coil Fender Stratocaster (tm), for example, the
middle and neck coils were reasonably similar in construction and
could be balanced. But the bridge coil was hotter, having a
slightly different structure to provide a stronger signal from the
smaller vibration of the strings near the bridge. Thus in one
experiment, even balancing the turns as closely as possible
produced a signal with phase differences to the other two pickups,
due to differences in coil impedance.
A previous patent (U.S. Pat. No. 9,401,134, 2016, Baker), which
supports this invention, used the concept of humbucking pairs and
switching systems for four single-coil electromagnetic pickups with
coils of equal turns. Baker modified standard single-coil pickups,
adding turns until four single-coil pickups have a reasonably equal
response to external AC fields, and shocked the magnets of two of
them, with a stronger rare-earth magnet, to reverse the poles,
providing two matched pickups with North poles toward the strings
(N-up) and two matched pickups with South poles toward the strings
(S-up). Limited to two 4P5T lever switches, that system had no
out-of-phase, or contra-phase, humbucking pairs, but four
humbucking pairs and one humbucking quad of parallel-connected
pickups on one 5-way switch, and four series-connected pairs with a
series-parallel connected quad on the other 5-way switch.
The NP patent application Ser. No. 15/616,396 (Baker, 2017),
Humbucking switching arrangements and methods for stringed
instrument pickups, extended this invention to humbucking quads,
hexes, octets and up, as well as the special case of a humbucking
triple. It makes clear that that any electronic switching system
for electromagnetic sensors must know which pole is up on each
pickup in order to achieve humbucking results. The NP patent
application Ser. No. 15/917,389 (Baker, 2018), Single-Coil Pickup
with Reversible Magnet & Pole Sensor, presented embodiments of
single-coil pickups with magnets that could be removed and
reversed, providing as well a signal for the state of the
reversal.
For two matched pickups, the humbucker connections, either series
or parallel, must be contra-phase if they have the same poles up,
and in-phase of they have different poles up. For K number of
matched pickups, this makes possible K*(K-1)/2 pair combinations,
regardless of poles or series-parallel connections. For example,
for four matched pickups A, B, C & D, the unique pair
combinations are AB, AC, AD, BC, BD and CD, or 4*3/2=6. If they all
have the same pole up, i.e., (N,N,N,N), then all the combinations
are contra-phase, and moving any pickup to any other position has
no effect. If they have one pole different, i.e., (N,S,S,S), then
that pole can be moved to 4 different positions. If they have 2
poles different, i.e., (N,N,S,S), then those poles can be placed
uniquely only as (N,N,S,S), (N,S,N,S) and (N,S,S,N), since
reversing the poles, i.e., (S,S.N,N), (S,N,S,N) and (S,N,N,S)
produce exactly the same in-phase and contra-phase humbucking pair
combinations. This total 8 different pole configurations. (See
also,
https://www.researchgate.net/publication/323686205_Making_Guitars_with_Mu-
ltiple_Tonal_Characters)
It turns out that if the pickup poles are reversible, for K number
of pickups, there can be 2.sup.K-1 different pole configurations,
each configuration producing K*(K-1)/2 humbucking pairs, each
configuration producing K*(K-1) potentially unique humbucking
tones, if both series and parallel pair connections are considered.
But all the pole configuration have some common tones. There can be
only 2*K*(K-1) potentially unique humbucking tones from the
2.sup.K-1 different pole configurations. For 5 pickups, this is 16
different pole configurations, with 20 potentially unique
humbucking pair tones for each configuration, with a total of 40
unique humbucking pair tones for the entire set. For K>7, the
number of pole configurations exceeds the number of potentially
unique tones.
Even for just humbucking pairs, never mind triples, quads, quintets
and hextets, it would be a challenging problem for either
electro-mechanical or digitally-controlled pickup switching systems
to take full advantage of reversible pickup poles.
Electro-Mechanical Guitar Pickup Switching
The standard 5-way switch (Gagon & Cox, U.S. Pat. No.
4,545,278, 1985) on an electric guitar with 3 single-coil pickups
typically provides to the output: the neck coil, the neck and
middle coils in parallel, the middle coil, the middle and bridge
coils in parallel, and the bridge coil. Typically, the middle
pickup has the opposite pole up from the other two, making the
parallel connections at least partially humbucking. But while the
middle and neck coils have roughly equal numbers of turns, and the
bridge coil has more turns than the other two to produce a roughly
equal signal from the smaller physical vibrations of the strings
nearer the bridge. The standard 3-way switch on a dual-humbucker
guitar typically produces the neck, neck.parallel.bridge and bridge
pickups at the output, all of which are humbucking.
These two switches are "standards" because the vast majority of
electric guitars on the market use them. There are other switching
systems, such as U.S. Pat. No. 3,290,424, Fender, 1966; U.S. Pat.
No. 4,305,320, Peavey, 1981; U.S. Pat. No. 5,136,918, Riboloff,
1992; U.S. Pat. No. 5,311,806, Riboloff, 1994; U.S. Pat. No.
5,763,808, Thompson, 1998; U.S. Pat. No. 6,781,050B2, Olvera, et
al., 2004; US2005/0150364A1, Krozack, et al.; U.S. Pat. No.
6,998,529B2, Wnorowski, 2006; and US2009/0308233A1, Jacob. But they
are either not on the market, or fill niche positions. In any case,
they do not intersect or interfere with the switching systems
presented here.
Microcontrollers in Guitar Pickup Switching
Ball, et al. (US2012/0024129A1; U.S. Pat. No. 9,196,235, 2015; U.S.
Pat. No. 9,640,162, 2017) describe a "Microprocessor" controlling a
"digitally controlled analog switching matrix", presumably one or
more solid-state cross-point switches, though that is not
explicitly stated, with a wide number of pickups, preamps and
controls hung onto those two boxes without much specification as to
how the individual parts are connected together to function.
According to the Specification, everything, pickups, controls,
outputs and displays (if any), passes through the "switching
matrix". If this is comprised of just one cross-point switching
chip, this presents the problem of inputs and outputs being
interrupted by queries to the controls. In the Specification, the
patent cites the ability to make "any combination of combinations"
without describing or providing a figure any specific one, or even
providing a table or scheme describing the set. It states, "On
board controls are similar to or exactly the same as conventional
guitar/bass controls." But there is not enough information in the
patent for someone "with ordinary skill in the art" to either
construct or fully evaluate the invention.
The Ball patents make no mention or claim of any connections to
produce humbucking combinations. The flow chart, as presented,
could just as well be describing analog-digital controls for a
radio, or record player or MPEG device. In later marketing
(https://www.music-man.com/instruments/guitars/the-game-changer),
the company has claimed "over 250,000 pickup combinations" without
demonstration or proof, implying that it could be done with 5 coils
(from 2 dual-coil humbuckers and 1 single-coil pickup).
Baker (NP patent application Ser. No. 15/616,396, 2017)
systematically developed series-parallel pickup topologies from 1
to 5 coils, with 6 coils in notes not included. (See also
https://www.researchgate.net/publication/323390784_On_the_Topologies_of_G-
uitar_Pickup_Circuits) The table labeled Math 12b in that
application shows that 5 coils can produce 10717 unique circuits of
sizes from 1 to 5 coils, including reversals of individual pickup
terminals and moving pickups around the circuit positions. Math 12b
shows that 6 coils can produce 286,866 unique circuits of from 1 to
6 coils. "Over 250,000" circuits are possible only with 3
humbuckers, or with 5 coils and a piezoelectric pickup.
Bro and Super, U.S. Pat. No. 7,276,657B2, 2007, uses a
micro-controller to drive a switch matrix of electro-mechanical
relay switches, in preference to solid-state switches. The
specification describes 7 switch states for each of 2 dual-coil
humbuckers, the coils designated as 1 and 2: 1, 2, 1+2 (meaning
connected in series), 1-2 (in series, out-of-phase), 1.parallel.2
(parallel, in-phase), 1.parallel.1(-2) (parallel, out-of-phase), 0
(no connection, null output). In Table 1, the same switch states
are applied to 2 humbuckers, designated neck and bridge. That is
three 7-way switches, for a total number of combinations of
7.sup.3=343.
In this arrangement, null outputs occur when a series connection is
broken. This will happen once for all 3 switches set to null, and
each time a series connection in the last switch is broken by a
null output in the previous two switches, for a total of at 5 null
outputs. Although Super has argued via unpublished e-mail that a
reversed output connection is a separate tone, this inventor calls
it a duplicate. This can happen when the 7-way output switch is set
to parallel and out-of-phase for the second humbucker, the first
humbucker 7-way switch is set to null, and the second humbucker
7-way switch is set to any output, or 6 combinations. Taking out 5
nulls and 6 duplicates that leaves 332 useful combinations.
Table 1 in Bro and Super cites 157 combinations, of which one is
labeled a null output. For 4 coils, the table labeled Math 12b in
Baker, NP patent application Ser. No. 15/616,396, 2017, identifies
620 different combinations of 4 coils, from 69 distinct circuit
topologies containing 1, 2, 3 and 4 coils, including variations due
to the reversals of coil terminals and the placement of coils in
different positions in a circuit. Baker shows how an all-humbucking
20-combination electromechanical switching circuit for two
humbuckers produces mean frequencies for 6 strummed strings which
have 3 or 4 duplicate tones, with a tendency for mean frequencies
to bunch at the warm end of the scale. The use of mean frequency in
this manner has not yet been established as a measure of tone, but
as a first approximation still raises the question of the practical
use of so many tones so close together.
Baker, NP patent application Ser. No. 15/616,396, 2017,
demonstrates, in the table labeled Math 31, that the total number
of potentially distinct humbucking tones from topologically
different electrical circuits of matched guitar pickups, using just
simple series-parallel topologies, can be up to 2 for 2 sensors, 6
for 3, 48 for 4, 200 for 5, 3130 for 6 and 19,222 for 7 sensors, up
to 394,452 for 8 sensors. Beyond 3 or 4 matched single-coil
pickups, electro-mechanical switches are too expensive and
impractical. One must us a cross-point matrix or switch of some
kind, preferably analog-digital. Baker offered an architecture for
a micro-controller system using a solid-state cross-point switch,
specifying how the switch is dedicated to sensors, noting that for
Mx/2 number of 2-wire sensors, an Mx by (My=Mx+2) crosspoint
switch, or larger, will cover all possible interconnections, and
provide a 2-wire output. But for humbucking circuits made of
matched single-coil pickups, as disclosed in that NPPA, the
orientation of the pickup magnetic poles to the strings must be
known by the microcontroller. This requires the pickup poles to be
manually assigned in the microcontroller switching or programming,
or for the microcontroller to directly detect the orientation of
the pickup poles. This programming problem has not yet been
solved.
Technical Problems to be Solved
Baker (NP patent application Ser. No. 15/616,396, 2017) developed
humbucking circuits for matched pickups only in humbucking pairs,
quads, hextets, octets and one special case of a humbucking triple.
The special case is important because it can be expanded to
quintets, septets, nine-tets and up, including series and parallel
combinations of humbucking pairs, quads and up with those circuits
of odd numbers of matched pickups. This expands the range of
possible matched-pickup humbucking circuits to any number of
pickups, odd or even. As disclosed in the NPPAs above, there are
many more possible non-humbucking series-parallel circuits than
humbucking, falling as the number of pickups increase. At 6
pickups, only 1.1% of the possible series-parallel circuits are
humbucking pairs, quads and hexes. So far, this inventor knows of
no micro-controller algorithm to use with a cross-point switch to
pick only humbucking circuits, and is precluded by medical
disabilities from developing one.
Having a large, even huge, number of possible circuits and tones to
pick from raises the question of how to do the picking, and how to
order them from warm to bright and back. Experiments with two
humbuckers suggest that tones, as measured by the mean frequency of
strummed strings, are much closer together at the warm end than the
bright end, and may be so close together that having a large number
of possible circuits and tones becomes a matter of diminishing
returns. Some method is needed to order and pick tones that are
sufficiently distinct to make efficient use of available and
invented switching methods, whether electro-mechanical or
digitally-controlled.
SUMMARY OF INVENTION--TECHNICAL PROBLEMS RESOLVED
This invention discloses hitherto unknown, non-obvious, beneficial
and eminently simple means and methods to solve those problems. It
comprises of simple circuits that are constructed and switched
according to Four Simple Rules: 1) all of the pickups or sensors
are connected to a common point at the pickup terminals that
present the same phase of external electro-magnetic interference,
or "hum"; 2) at least two pickups must be in the circuit, connected
at least one from the common point to the output low terminal, and
the other(s) at least one connected from the common point to the
output high terminal; and 3) either the common point must be
grounded, or the low terminal of the output must be grounded, but
not both; and 4) the pickups or sensors must be matched, all having
the same response to external hum.
Preferably, but not necessarily, some of the sensors, or pickups,
will have desired signal phases that are opposite from one another,
with respect to the common connection point. If the signal phases
of two sensors are opposite, and one is connected to the high
output terminal and the other is connected to the low output
terminal, then the signal voltage difference across the output
terminals is in-phase. If both sensors have the same signal phase,
then the voltage difference across the output terminals is
out-of-phase, or contra-phase. It turns out that any number of
matched sensors can be connected to the common connection point and
the output terminals in this manner, whether by electro-mechanical
or digitally-controlled means, and the hum voltages will cancel.
Additionally, this kind of circuit can be connected in series or
parallel with any other humbucking circuit, and the output will
remain humbucking. This greatly expands the number of possible
humbucking circuits from pairs, quads, hexes and above, using any
even or odd number of sensors.
While this invention was developed primarily for matched
single-coil electromagnetic guitar pickups, it has much wider
application. It can be applied to any type of sensor which follows
the same rules, in any application where matched sensors can be
used in this manner to reject external interference.
In the case of an electromagnetic guitar pickup, some effort has
been made in the past to connect the outer windings of the coil to
ground, so as to provide a kind of shield to electric field noise.
But when those pickups are connected in series, this is not
possible for all the pickups in the circuit, so that stratagem
fails. Only one of the pickups in series can be connected to
ground, it any. More often, in better quality pickups, copper or
aluminum foil is wrapped about the outside of the coil and
grounded. In the case of this invention, where the common
connection point is grounded and output is differential, that
stratagem succeeds.
Also, many patents and explanatory texts claim that the windings of
coil with opposite magnetic polarities are reversed to achieve
humbucking. This is not truly necessary; only the terminals of the
pickup need be reversed. It makes less manufacturing sense to have
two sets of coil winding machines, winding coils in opposite
directions. In the case of a grounded common connection point, this
invention fully justifies that economy. No terminals need be
reversed, only the magnetic field, as described in NP patent
application Ser. No. 15/917,389 (Baker, 2018).
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A-B show a convention for drawing matched vibration sensors
in an electronic circuit, including the equal signals from external
noise, Vn, the matched sensor impedance, Z, the vibration signal
from an N-polarity sensor, V.sub.N (1A), and the vibration signal
from a matched S-polarity sensor, V.sub.S (1B), with respect to
high (+) and low (-) sensor terminals.
FIG. 2 shows a grounded common connection point (1) with j number
of matched sensors connected between it and the high switching
output (V1, Vo+), and with k number of matched sensors between the
common connection point and the low switching output (V2, Vo-).
Only the noise signals are shown, to emphasize that they oppose at
the output, which is loaded by a resistance R.sub.L.
FIG. 3 shows a similar circuit to FIG. 2, with only the vibration
signal voltages showing, and with j number of N-up matched sensors
between the common connection point (1) and Vo+, k number of N-up
sensors between the common connection point and Vo-, 1 number of
S-up matched sensors between the common point and Vo+, and m number
of S-up sensors between the common point and Vo-, with Vo loaded by
resistor, R.sub.L.
FIG. 4 shows the physical setup for a two-humbucker experiment,
with the one mini-humbucker (5) at the neck (1), with adjustable
N-up screw poles (N1) and S-up non-adjustable flat poles (S1),
another reasonably-matched humbucker of the same model (7), with
reasonably matching characteristics, at the bridge (3), with N-up
screw poles (N2) and S-up flat poles (S2), showing the position and
direction of strumming used on all six strings (11).
FIG. 5 shows a representative test setup for the common connection
point (1) system to get a Fast Fourier Transform (FFT) magnitude
spectrum from the N-up matched pickup (N1) indicated in FIG. 4
connected between the common point and the left microphone input
(LEFT) of a desktop computer, through a voltage-follower amp (U1),
and from the two S-up matched pickups (S1 & S2) connected
between the common point and the right mic input (RIGHT) through a
voltage follower (U2).
FIG. 6 shows the plot of mean frequencies of the FFT spectra,
developed by the experiment in FIG. 5 for the 25 combinations of
pickup circuits, using common connection point switching, ordered
from low to high, with the roughly equivalent frequencies of a
standard 3-way switch on a dual-humbucker guitar, marked as Neck
HB, Neck.parallel.Bridge, and Bridge HB.
FIG. 7 shows a 4 pole 6 throw (SW1) switching circuit using an
ungrounded common connection point (1) with two N-up
electromagnetic coil matched pickups (N1 & N2) and a matched
S-up pickup (S1), where three poles and throws of the switch make
all 6 combinations of the pickups in the order N1-N2, N2+S1, N1+S1,
N2+(S1-N1)/2, N1+(S1-N2)/2 and (N1+N2)/2+S1, where the pickup
designations also represent their vibration signals, with the
4.sup.th pole and throws switching the tone capacitors C.sub.T1 and
C.sub.T2 to the tone pot P.sub.T, the output connected to the
volume pot, P.sub.V, with a single-ended output, Vo, referenced to
ground.
FIG. 8 shows the common connection point (1) switching circuit,
like FIG. 7, with the on-switch wired interconnects on a 4P6T
switch, SW2, replaced by a printed circuit board (13) and plug
(15). The 6 throws for the 3 poles connected to matched pickups N1,
S1 and N2, pass to the board with vertical wires on one side of the
board and horizontal wires on the other side, connected by soldered
through-board jumpers (black dots) to make connections to the high
output terminal (17, Vo+) or the low output terminal (19, Vo-). The
6 throws for the 4.sup.th pole connect to the board to switch
adjustment components, X1 to X6, to the adjustment output (Xn). The
jumpers (J1, J2) connect the system ground either to the common
connection point (1) to make the output (Vo) differential, or to
Vo- to make the output single-ended.
FIG. 9 shows two matched N-up pickups (N1 & N2) and two matched
S-up pickups (S1 & S2) with attached individual tone circuits
(T1 to T4) connected between an ungrounded common connection point
(1) and the grounded volume control pot (P.sub.V) to the
single-ended output (Vo) through the 4P6T switch (SW3). In the
order of throws, 1 to 6 respectively, the connections produce the
circuits: N1+(S1+S2-N2)/3, N1+(S1+S2)/2, N1+S2,
(N1+N2)/2+(S1+S2)/2, N1+(S1-N2)/2 and (N1-S1)/2+(S2-N2)/2, where
the pickup designation also represent their vibration signals.
FIG. 10 shows a circuit similar to FIG. 7, with matched pickups N1,
S1 and N2, having individual tone circuits, T1, T2 and T3,
comprised each of a tone capacitor (C.sub.Ti) and a tone pot
(R.sub.Ti), connected to a 4P6T switch (SW4) with three poles and
their throws producing the same pickup circuit connections as in
FIG. 7, and the fourth pole and throws connecting gain resistors
(RG1 to RG6) to an output preamp (U1) with a feedback resistor
(R.sub.F). The single-ended output of the preamp circuit drives the
circuit output (Vo) through a volume pot (P.sub.V).
FIG. 11 shows a similar circuit to FIG. 10, but with the common
connection point (1) grounded, and the switch (SW5) output
(V.sub.S+, V.sub.S-) connected to a differential input,
single-ended output amplifier comprised of the differential input
section (U1, U2, R.sub.F, R.sub.F, R.sub.Gi) and the single-ended
output section (U3, R.sub.F, R.sub.F, R.sub.F, R.sub.F), feeding
through a volume pot (P.sub.V) to the single-ended output (Vo).
FIG. 12 shows three matched dual-coil humbucking pickups (N1S1,
N2S2, N3S3), with their center tap connected to the common
connection point (1), which is either grounded or not, depending on
whether the output of the 6-pole X-throw switch (SW6) is intended
to be single-ended (not grounded) or differential (grounded). Only
the first poles are shown.
FIG. 13 shows two humbucking pickups (N1S1, N2S2) with center taps
connected to a grounded common connection point (1), and through
the connections of a 6P6T switch (SW6) to the differential switch
output (.DELTA.V.sub.S), which is connected to a differential
amplifier, comprised of operational amplifiers sections U1a and
U1b, two feedback resistors (R.sub.F,R.sub.F) and a gain resistor
(R.sub.Gi), which is switched by SW6 among gain resistors R.sub.G1
to R.sub.G6. One pole and the related throws of SW6 connect tone
capacitors C.sub.T1 to C.sub.T6 to either Tone Circuit 1 (a
resonant capacitor, C.sub.Ti) or Tone Circuit 2 (a tone capacitor,
C.sub.Ti, and a tone pot, P.sub.T), which is situated at the output
of the switch, .DELTA.V.sub.S. The output of the differential
amplifier is .DELTA.Vo.
FIGS. 14A-B show symbolic functional (above) and circuit block
(below) diagrams for digitally-controlled analog solid-state
switches with 1P2T (14A) and 1P3T (14B), along with the logic state
diagrams (S Out, 14A; S1 S0 Out, 14B) for those switches,
respectively. In all cases, A is the input and S, S0 and S1 are the
digital level control signals. NO means normally open and NC means
normally closed.
FIGS. 15A-B show circuits for single-ended (15A) and differential
(15B) amplifiers, with inputs Vs and outputs Vo, using operational
amplifiers (U1, U2ab), a gain resistors (R.sub.G) and feedback pots
(P.sub.F, P.sub.Fab), especially digitally-controlled pots. In FIG.
15B, pot P.sub.Fab is a two-gang pot, with sections that change
equally together.
FIGS. 16A-B show two versions of digitally-controlled switched tone
controls, using the solid-state switches from FIGS. 14A-B. FIG. 16A
shows three 1P2T switches (SWd, SWe, SWf), switching three tone
capacitors (C.sub.T1, C.sub.T2, C.sub.T3) to a tone pot (P.sub.T),
driven by 3 lines of I/O from a micro-controller (uC). The tone
circuit is connected across the signal (V.sub.S+, V.sub.S-) at the
output of a pickup switching system. FIG. 16B shows the same
micro-controller and same tone capacitors switching the tone
capacitors to a digitally-controlled pot (P.sub.TD) with 2 lines of
uC I/O control going to the switch (SWg), and 3 lines of uC I/O
control going to the pot.
FIG. 17 shows a micro-controller (uC) driving a common connection
point (1, C in a triangle) solid-state switching system, with 1P3T
switches SW1 to SWj, for N-up matched pickups, N1 to Nj, and 1P3T
switches SWj+1 to SWj+k for S-up matched pickups S1 to Sk. The
switch outputs are Vs+ and Vs-, which can be differential or
single-ended according to the digitally controlled 1P2T ground
switch, SWa. The 1P2T switch, SWb, shorts out the lower output
pickup coils to the common point (1), to allow for the measurement
of single or multiple parallel pickups. The output of the switching
system passes through an ANALOG CIRCUITS section, made up of parts
of previous figures, with uC controls for gain adjustment, to the
single-ended output, Vo. The uC has I/O controls for USER CONTROLS
& DISPLAY for the use interface, an analog-to-digital converter
(A/D), a math processing unit (MPU), which can be an external
co-processor, necessary for taking A/D signal samples to produce
FFT spectra to use in ordering tones. A digital-to-analog (D/A)
section feeds inverse-FFT audio signals into the Analog Circuits
section for output to help the user recall the tones for individual
pickup circuits. One section of I/O handles EXTERNAL
COMMUNICATIONS, by which the uC can be tested and reprogrammed, and
engage in other useful functions, such as allowing the user to use
other keyboard and computer devices to control it and the switching
circuit.
DESCRIPTION OF THE INVENTION
Principles of Operation
The principles of operation are mostly mathematical expositions
which cannot be patented. But they are necessary to discuss, as
they enhance understanding of the material invention, and define
the theoretical limits of the invention. Furthermore, they
demonstrate that the operation of instruments such as electric
guitars have not yet begun to find their limits. They can be a lot
more versatile than they are now.
FIG. 1 shows the sign conventions used in this work for matched
single-coil electromagnetic guitar pickups, and applies to any
other type of sensor which can be manufactured and mounted to
comply with the Four Rules described above. FIG. 1A shows the
convention for a pickup with a North magnetic field towards the
strings (N-up), and FIG. 1B shows a pickup with a South magnetic
field towards the strings (S-up). The coil impedance, Z, and
response to external noise, Vn, are matched in both pickups, while
the signal voltage for the N-up pickup, V.sub.N, is the opposite
polarity of the signal voltage for the S-up pickup, V.sub.S. Note
that the pickup terminal polarity is taken to be the same as the
external noise signal, Vn.
FIG. 2 shows the generalized circuit, considering only the noise
signal, Vn, the same in each pickup, with j number of pickups
connected between the grounded common connection point (1) to the
high terminal of the output, V1, and k number of pickups connected
between the common point and the low output terminal, V2. The
differential output voltage, Vo=V1-V2. Math 1 shows the circuit
equations and solution, developed in the symbolic math package,
Maple V, Release 4.00c, 1996. Thus the circuit is proven to be
humbucking, so long as the rules are followed.
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times..times..times..times..times..-
times..times..times..times..times..times..times..times..times..times..time-
s..times..times..times..times..times..times..times..times.
##EQU00001##
FIG. 3 shows the generalized circuit, considering only the string
vibration signals. The numbers j and k are redefined. Between the
grounded common connection point (1) and V1 there are j number of
N-up pickups, with signals V.sub.N1i, i=1 to j, and k number of
S-up pickups with signals V.sub.S1i, i=1 to k. Between the common
point and V2 there are 1 number of N-up pickups with signals,
V.sub.N2i, i=1 to 1, and m number of S-up pickups with signals,
V.sub.S2i, i=1 to m. The differential output voltage Vo=V1-V2. Math
2 shows the circuit equations and the solution for Vo. It shows
that the N-up pickups on the top are in phase with the S-up pickups
on the bottom, but out of phase with the S-up pickups on the top
and the N-up pickups on the bottom.
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times..times..times..times..times..-
times..times..times..times..times..times..times..times..times..times..time-
s..times..times..times..times..times..times..times..times..times..times..t-
imes..times..times..times..times..times..times..times..times..times..times-
..times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times. ##EQU00002##
Circuits with Two Coils
With any two coils, (N1,N2), (N1,S1) or (S1,S2), indicating the
available coils with either N-up or S-up fields, there is only one
possibility, or the single combination of 2 things taken 2 at a
time; one coil connects to the high output terminal and the other
to the low output terminal. Let the first number represent the
upper coil and the second the lower coil. Reversing those
connections only changes the sign of the output signal. This
inventor contends that this produces no effective difference in
tone. Human ears cannot tell the differences in the phase of a
signal producing a tone without some other external reference.
Therefore, such changes do not count. And going forward, this will
in fact reduce the number of choices when the numbers of coils
connected to the high and low terminals of the output are equal.
Note that when the coils have the same poles up, the switching
circuit correctly produces an out-of-phase, or contra-phase,
signal, such as N1-N2.
Circuits with Three Coils
Suppose that the three coils can be represented by the designations
N1, S1 and N2, for 1 S-up and 2 N-up coils. They can be connected
through the switching system to the output terminals as either 2
coils or 3 coils. Table 1 shows various possible circuit/switching
combinations. Note that reversing the output terminals produces the
duplicates in the right three columns of the table. It does not
matter if the circuits are switched this way; it only matters that
duplicates are not counted as separate circuits and possible tones.
This might be called the Fifth Simple Rule, but it might wait until
actual human trials are conducted to confirm it. Call it instead
the Rule of Inverted Duplicates.
TABLE-US-00001 TABLE 1 Circuit/switching combinations for three
coils, N1, S1 and N2, with upper coils connected from the common
connection point to the high output terminal, and lower coils
connected from the common point to the low output terminal.
Duplicates 2 N1 N1 S1 S1 N2 N2 coils S1 N2 N2 N1 N1 S1 3 N1 S1 N2
S1N2 N1N2 N1S1 coils S1N2 N1N2 N1S1 N1 S1 N2
Note that in Table 1, for 2 coils, the results for 2 coils can be
explained as (3 things taken 1 at a time) times the number of
combinations for 2 coils, or 3*1=3. The results for 3 coils can be
taken as (3 things taken 1 at a time)*(2 things taken 2 at a time),
or 3*1=3. The combined results for 3 coils, taken in pairs and
triples, is 6 humbucking circuits. By Math 2, for the first column
of 2 coils, Vo=V.sub.N1+V.sub.S1, for the first column of 3 coils,
Vo=V.sub.N1+(V.sub.S1-V.sub.N2)/2, and for the second column of 3
coil duplicates, Vo=(V.sub.N1+V.sub.N2)/2+V.sub.S1. The Rule of
Inverted Duplicates also applies to reversals of all the magnetic
poles.
It still works for all pickups N-up, N1, N2 and N3, as shown in
Table 2, shown without the duplicates. By Math 2, the first column
of 2 coil combinations has an output voltage of
Vo=V.sub.N1+V.sub.N2. The first column of 3 coil combinations has
an output voltage of Vo=V.sub.N1-(V.sub.N2+V.sub.N3)/2.
TABLE-US-00002 TABLE 2 Circuit/switching combinations for three
N-up coils, N1, N2 an N3, with upper coils connected from the
common connection point to the high output terminal, and lower
coils connected from the common point to the low output terminal. 2
coils 3 coils N1 N1 N2 N1 N2 N3 N2 N3 N3 N2N3 N1N3 N1N2
The Rule of Inverted Duplicates also applies to reversals of all
the magnetic poles. If Table 1 had instead been constructed of 1
N-up and 2 S-up pickups, S1, N1 and S2, replacing N1, S1, and N2 at
their respective positions, the signal voltages at all those
positions would simply be reversed. But as NP patent application
Ser. No. 15/917,389 (Baker, 2018) demonstrates, the odd pole pickup
can be placed in three different physical positions, providing
different tonal characters for the entire set.
Circuits with Four Coils
Suppose that we have four matched pickups designated N1, S1, N2 and
S2. We can calculate the number of possible outputs for pairs and
triples by taking 4 things 2 at a time and 4 things 3 at a time,
multiplied by the number of possible pairs (1) and triples (3)
without extra pickups. Math 3 shows this calculation.
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times. ##EQU00003##
There are 2 ways to arrange 4 coils in a humbucking quad: 1) a
single coil in series with (or over) 3 coils in parallel, and 2) 2
coils in parallel, the pair in series with (or over) another 2
coils in parallel. Putting 3 coils in parallel over 1 coil would
merely duplicate the first instance by the Rule of Inverted
Duplicates. This will be true for any number of pickups J. If we
follow the convention of putting the smaller number of pickups over
the larger or equal, the number of pickups connected to the high
output terminal will range from range from 1 to J/2-1 for J odd,
and 1 to J/2 for J even. Table 3 shows the switched combinations
for J=4, given 2 N-up pickups N1 and N2, and 2 S-up pickups, S1 and
S2.
TABLE-US-00003 TABLE 3 Switching/combinations for 4 coils, N1, S1,
N2 and S2 1 over N1 N2 S1 S2 3 N2S1S2 N1S1S2 N1N2S2 N1N2S1 Vo =
V.sub.N1 + V.sub.N2 .sup.+ -V.sub.S1 + -V.sub.S2 + (V.sub.S1 +
V.sub.S2 - V.sub.N2)/3 (V.sub.S1 + V.sub.S2 - V.sub.N1)/3 (V.sub.S2
- V.sub.N1 - V.sub.N2)/3 (V.sub.S1 - V.sub.N1 - V.sub.N2)/3
duplicates 2 over N1S1 N1N2 N1S2 S1N2 S1S2 N2S2 2 N2S2 S1S2 S1N2
N1S2 N1N2 N1S1 Vo = (V.sub.N1 - V.sub.S1)/2 + (V.sub.N1 +
V.sub.N2)/2 + (V.sub.N1 - V.sub.S2)/2 + (V.sub.N2 - V.sub.S1)/2 +
(-V.sub.S1 - V.sub.S2)/2 + (V.sub.N2 - V.sub.S2)/2 + (V.sub.S2 -
V.sub.N2)/2 (V.sub.S1 + V.sub.S2)/1 (V.sub.S1 - V.sub.N2)/2
(V.sub.S2 - V.sub.N1)/2 (-V.sub.N1 - V.sub.N2)/2 (V.sub.S1 -
V.sub.N1)/2
An example of 5 coils can be 2 humbuckers and a single, which a
number of guitars on the market have. The number of 1-over-3
combinations can be calculated as (4 things taken 1 at a time)
times (3 things taken 3 at a time), or 4*1=4. The number of 2-over2
combinations can be calculated as one-half times (4 things taken 2
at a time) times (2 things taken 2 at a time), or 6*1/2=3, for a
total of 7 humbucking circuits from 4 pickups. Note that when all
the terms are collected for the 2-over-2 circuits, Vo for the
duplicates is the negative of Vo for the first three, due again to
the Rule of Inverted Duplicates. This will happen whenever j=k for
j-over-k circuits.
Circuits with 5 Coils
For 5 coils, one can take the previous numbers of tonal circuits
calculated for 2, 3 and 4 coils and multiply them by 5 things taken
2, 3 and 4 at a time, plus the number of possibilities for
combinations of 5 coils. Unique combinations of 5 coils or pickups
in this switching system can be "quint" combinations of 1-over-4
and 2-over-3, without duplicate inversions. Math 4 shows these
calculations:
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times..times..times..times..times..-
times..times..times..times..times..times..times..times..times..times..time-
s..times..times..times..times..times..times..times..times..times..times..t-
imes..times..times..times..times..times..times..times..times..times..times-
. ##EQU00004##
Circuits with 6 Coils
A number of guitars on the market have three humbuckers, which can
be considered 6 matched pickups for this discussion. Math 5 shows
these calculations. Not the reduction of 3-over-3 hextets due to
the Rule of Inverted Duplicates.
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times..times..times..times..times..-
times..times..times..times..times..times..times..times..times..times..time-
s..times..times..times..times..times..times..times..times..times..times..t-
imes..times..times..times..times..times..times..times..times..times..times-
..times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times. ##EQU00005##
Fender (U.S. Pat. No. 3,290,424, 1966) managed to put 8 sets of
poles under a pick guard, which arguably could have been 8 pickups.
Whether or not it would be useful is another matter. For stringed
instruments like pianos, where many more pickup coils can be used
along the strings, the method of calculating the number of possible
humbucking circuits can be easily expanded by the same rules. So
for 2, 3, 4, 5, 6, 7, 8, 9 and 10 matched pickup coils, this
switching system can produce, respectively, 1, 6, 25, 90, 301, 966,
3025, 9330 and 28,501 humbucking circuits. The natural logs of the
number of HB circuits, NHB, are about: 0, 1.79, 3.22, 4.50, 5.70,
6.87, 8.01, 9.14 and 10.26. So the rise in the number of circuits
is clearly an exponential function of the number of pickups.
TABLE-US-00004 TABLE 4 Numbers of circuits for K pickups taken J at
a time in a common connection point switching circuit. J = K 2 3 4
5 6 7 8 9 10 11 12 Totals 2 1 1 3 3 3 6 4 6 12 7 25 5 10 30 35 15
90 6 15 60 105 90 31 301 7 21 105 245 315 217 63 966 8 28 168 490
840 868 504 127 3025 9 36 252 882 1890 2604 2268 1143 255 9330 10
45 360 1470 3780 6510 7560 5715 2550 511 28501 11 55 495 2310 6930
14322 20790 20955 14025 5621 1023 86526 12 66 660 3465 11880 28644
49896 62865 56100 33726 12276 2047 261625
Table 4 shows these calculations for this kind of circuit extended
to K pickups taken J at a time, where K=2 to 12 and J=2 to 12. The
first thing that becomes apparent is that for J pickups taken J at
a time, the number of circuits is 2.sup.(J-1)-1. Math 6 shows the
full equation. This determines the upper limit of switched circuits
of this type.
.times..times..times..times..times..times..times..times..times..gtoreq..t-
imes..times..times..times..times..times..times..times.>.times..times..t-
imes..times..gtoreq..times..times..times..times..times..times..times..time-
s..times..gtoreq..gtoreq..times..times..times..times..times..times..times.-
.times. ##EQU00006##
Hybrid Humbucking Circuits
Using matched pickups, common connection point humbucking circuits
can be combined in series and parallel with the kind of
series-parallel humbucking circuits disclosed in NP patent
application Ser. No. 15/616,396 (Baker, 2017), and the result will
still be humbucking. Thus humbucking quintets can be constructed by
placing humbucking pairs in series and in parallel with a
humbucking triple. Humbucking septets can be formed by placing
humbucking quads in series with humbucking triples, and by placing
humbucking pairs in series and parallel with humbucking pairs.
Humbucking nine-tets can be formed by placing humbucking sextets in
series and parallel with humbucking triples, by placing humbucking
quints in series and parallel with humbucking quads, and by placing
humbucking septets in series and parallel with humbucking
pairs.
This is less a matter of constructing new circuits than expanding
the number of humbucking circuits that can be obtained by replacing
unmatched pickups with matched pickups in all series-parallel
circuits. In general, hybrid humbucking circuits cannot take
advantage of the Four Simple Rules for the switching system
disclosed here.
The Number of Possible Tones with Reversible Pickup Poles
NP patent application Ser. No. 15/917,389 (Baker, 2018) shows that
for J number of matched pickups with reversible poles, there are
2.sup.J-1 possible pole configurations: 2 configurations for 2
pickups, 4 for 3 pickups, 8 for 4 pickups, 16 for 5 pickups, and so
forth. Suppose the one has matched pickups with reversible poles in
positions A, B, C, D, . . . , where A is N-up and A' is S-up. Each
position picks up fundamentals and harmonics of vibration that are
at least slightly different in tonal content. How many different
circuit-pole combinations have possibly different tones? For 2
pickups, there is only 1 circuit with 2 possibilities, A+B' and
A-B, where A, B and B' also stand in for the signal voltages.
For 3 pickups, there are 4 pole position configurations: (A,B,C),
(A',B,C), (A,B',C) and (A,B,C'). Table 5 shows the results. The
first pickup in the pole position sequence is assumed to be
connected between the common connection point and the high output
terminal. For humbucking pairs, there are only 6 possible tonal
differences, because of duplicates, like A-B, and the Rule of
Inverted Duplicates, i.e., -A'-B=A+B'. To look at it another way,
there are only unique three pairs, and A.+-.B allows for 2 choices,
or 3*2=6. For any pole configuration, there are 3 switched pairs,
each of which produces a set of 3 potentially unique tones out of
6. The lower half of Table 5 shows how a 1-over-2 humbucking triple
produces 3 possible triples with 12 possible tones. The
possibilities go as A.+-.(B.+-.C)/2, or 2.sup.2=4 sign choices, and
3 circuit choices for 3*4=12 unique circuits with potentially
unique tones. We must say "possible tones", or "potentially unique
tones", because the following experiment with two humbuckers
demonstrates that some tonal results can be very close together. So
for 3 pickups, we have 18 potentially unique tones, from 4
different pole configurations, each of which has 6 switched
circuits with a set of 6 of those 18 potentially unique tones.
TABLE-US-00005 TABLE 5 Possible different tonal circuits for 3
matched pickups, where A means a N-up pickup and A' means a S-up
pickup A, B, C A', B, C A, B', C A, B, C' A&B A - B -A ' - B A
+ B' * A - B * 3 out of A&C A - C -A' - C A - C * A + C' ** 6
possible B&C B - C B - C * -B' - C B + C' ** A&(B&C)/2
A + (-B - C)/2 -A' + (-B - C)/2 A + (B' - C)/2 A + (-B + C')/2 3
out of B&(A&C)/2 B + (-A - C)/2 B + (A' - C)/2 -B' + (-A -
C)/2 B + (-A + C')/2 12 possible C&(A&B)/2 C + (-A - B)/2 C
+ (A' - B)/2 C + (-A + B')/2 -C' + (-A - B)/2 * duplicate, **
inverted output duplicate
We can see that for 4 pickups, with four 1-over-3 circuits and
three 2-over-2 circuits, changing the pole configurations can only
change the signal phases as A.+-.(B.+-.C.+-.D)/3 and
(A.+-.B)/2.+-.(C.+-.D)/2, or 2.sup.3=8 signal sign configurations.
That means 7*8=56 potentially unique tones, plus those for 4
pickups taken 2 and 3 at a time. In general, if we have K number of
pickups, with 2.sup.K-1 number of pole configurations, we can have
signal phase changes at different positions that go as
A.+-.B.+-.C.+-. . . . .+-.K or 2.sup.K-1 possible phase changes for
each possible circuit, regardless of where the parentheses and
divisors go to fit the solution in Math 2. We cannot count
.+-.A.+-.B.+-.C.+-. . . . .+-.K, or 2.sup.K possible phase changes,
because of the Rule of Inverted Duplicates.
For humbucking pairs with 4 pickups, we have [4 pickups taken 2 at
a time]=6 pair combinations, times [2.sup.(2-1)-1]=1 circuits,
times 2.sup.(2-1)=2 phase changes, or 6*2=12 potentially unique
tones. For humbucking triples with 4 pickups, we have [4 pickups
taken 3 at a time]=4 triple combinations, times [2.sup.(3-1)-1]=3
circuits, times 2.sup.(3-1)=4 phase changes, or 4*3*4=48
potentially unique tones. This gives a total of 12+48+56=116
potentially unique tones, from 8 different pole configurations,
each of which has a set of 25 switched circuits, each of which has
a set of 25 of those 116 potentially unique tones.
.times..times..times..times..times..times..times..times..times..times.
##EQU00007##
Math 7 shows the total number of tones for K number of matched and
reversible pole single-coil pickups, for circuits of J=1 to K. The
first term in the summation is the number of circuits of K pickups
taken J at a time; the second term is the number of common-point
switched circuits for J pickups; and the third term is the number
of pickup sign changes obtained by changing poles in J pickup
positions. Table 6 shows the results of this equation in the Totals
column on the right. The first header row is J; the second is the
number of the number of pole configurations and pickup signal sign
changes for J pickups; and the third is the number of unique
circuits for J pickups in a common connection point switching
circuit. The Totals column represents the total number of
potentially unique tones possible for K pickups in circuits of size
J=2 to K.
TABLE-US-00006 TABLE 6 Number of potentially unique tones for K
matched and pole-reversible single-coil pickups for circuits of J =
2 to K pickups. J # in Ckt 2 3 4 5 6 7 8 9 10 2.sup.(J-1) 2 4 8 16
32 64 128 256 512 2.sup.(J-1) - 1 K # pickups 1 3 7 15 31 63 127
255 511 Totals 2 2 2 3 6 12 18 4 12 48 56 116 5 20 120 280 240 660
6 30 240 840 1440 992 3542 7 42 420 1960 5040 6944 4032 18438 8 56
672 3920 13440 27776 32256 16256 94376 9 72 1008 7056 30240 83328
145152 146304 65280 478440 10 90 1440 11760 60480 208320 483840
731520 652800 261632 2411882
TABLE-US-00007 TABLE 7 Compilation of results of Tables 4 and 6,
showing the number of pole configurations, total number of common
connection point switching circuits and total number of potentially
unique tones for K pickups, and all circuits from J = 2 to K. K #
pickups # pole config # switch ckts # tones 2 2 1 2 3 4 6 18 4 8 25
116 5 16 90 660 6 32 301 3542 7 64 966 18438 8 128 3025 94376 9 256
9330 478440 10 512 28501 2411882
Table 7 is self-explanatory. All the other columns tend to rise
exponentially with K. There are always fewer tones per circuits
than there are pole configurations. All tones are potentially
unique until proven so. No more than about 9 standard-size
single-coil pickups can fit in between the neck and bridge of a
standard length six-string electric guitar. But there will be
diminishing returns with the increasing number of pickups, since
having coils close together reduces the differences in harmonic
differences they see from a vibrating string. Plus their magnetic
fields tend to interfere, and they also become weak transformers
when side-by-side. Five or six may be the practical limit. Ten
matched pickups is likely practical only on un-fretted instruments
of much larger scale, such as pianos. Or, if the principles can be
applied to piezo-electric and other vibration pickups, to
instruments such as drums and horns. In any case, these limits
extend far beyond standard 3-way and 5-way switches.
An Experiment with Two Mini-Humbuckers
FIG. 4 shows the neck (1) to bridge (3) region on an electric
guitar with two generic Hofner-style mini-humbuckers (5&7)
installed under the strings (9). The neck pickup (5) and the bridge
pickup (7), have one set of adjustable screw poles for the N-up
poles, (N1) and (N2), with hemi-spherical heads that extend above
the pickup cover, and one set of rectangular S-up poles, (S1) and
(S2), that sit flush with the cover. Since both pickups are the
same model number, the coils are reasonably matched in response to
external hum. The strings are tuned to the standard E-A-D-G-B-E,
and were strummed midway between the pickups at (11). For
reference, Table 8 shows the string fundamental and harmonic
frequencies.
TABLE-US-00008 TABLE 8 String fundamental frequencies and harmonics
for standard EADGBE tuning (Hz) String fund 2nd harm 3rd harm 4th
harm 5th harm 6th harm 7th harm 8th harm E 82.4 164.8 247.2 329.6
412 494.4 576.8 659.2 A 110.0 220.0 330.0 440.0 550 660 770 880 D
146.8 293.6 440.4 587.2 734 880.8 1027.6 1174.4 G 196.0 392.0 588.0
784.0 980 1176 1372 1568 B 246.9 493.8 740.7 987.6 1234.5 1481.4
1728.3 1975.2 E 329.6 659.2 988.8 1,318.4 1648 1977.6 2307.2
2636.8
FIG. 5 shows a humbucking triple using coils N1, S1 and S2, with a
common connection point (1), and two voltage follower
preamplifiers, U1 and U2. The output of U1 represents the high
output terminal, going to the left microphone channel of the mic
input of a desktop PC. The output of U2 represents the low output
terminal, going to the right microphone channel. All of the 25
circuit combinations were tested. A shareware program, Simple Audio
Spectrum Analyzer v3.9, .COPYRGT. W. A. Sterr 2001-2006,
SpecAn_3v97c.exe, digitized the signal and produced a
magnitude-only FFT spectrum for the mic signal Vo/2=(Left-Right)/2.
It took Hann (raised cosine) windows of 4096 values at a rate of
8000 samples per second, providing a frequency resolution of about
2 Hz, over a range from 0 to 3998 Hz. It averaged all the windows
together to produce a discrete FFT spectrum, measured as dB full
scale (dBFS) versus frequency, exported into a *.CSV text file and
imported into MS Excel for processing.
Math 8 shows the equations used to process this FFT data in a
spreadsheet. There are 2048 magnitude values in the dBFS scale for
frequency bins from 0 to 3998 Hz, with a resolution of about 1.95
Hz. These are converted to linear values, linVn(fn), which are
summed to obtain the relative signal amplitude. Dividing each
magnitude by the total provides a probability density function,
Pv(fn), which sums to 1. Multiplying and summing over the product
of all the bin frequencies and the density function values gives
the mean frequency in Hz. The second and third moments of the FFT
spectrum are the bin frequency minus the mean, raised to the second
and third powers, times the density function. For the purpose of
simply maintaining smaller and more comparative numbers to consider
the second and third roots of the second and third moments have
units of Hz.
.function..times..times..times..times.<.times..times.<.times..times-
..times..times..times..times..times..times..times..times..times..times..ti-
mes..function..times..times..times..times..times..times..times..times..tim-
es..times..times..times..function..times..times..times..times..times..time-
s..times..function..times..times..times..times..times..times..times..funct-
ion..times..times. ##EQU00008##
Table 9 shows the results of this experiment for the 25 HB circuits
from the 4 coils in FIG. 4. The designation "o" between the pole
designations means "over", as in N1oS1, means that the N1 signal is
connected to the Left or high output in FIG. 5, and -S1 signal is
connected to the Right or low output in, providing the measured
output signal, Vo/2=(Left-Right)/2=(V.sub.N1+V.sub.S1)/2. Likewise,
S1oN1N2S2 indicates that the -V.sub.S1 signal is connected to the
high output, and the parallel connection of the signals V.sub.N1,
V.sub.N2 and -V.sub.S2 signals are connected to the low output,
providing a measured signal of
Vo/2=(Left-Right)/2=(-V.sub.S1+(V.sub.S2-V.sub.N1-V.sub.N2)/3)/2.
Hereafter, when the measured results are converted from dBFS to
linear, the linear results are multiplied by 2, and the "/2" is
dropped. The relative amplitudes in Table 9 have been multiplied by
2 after calculation to get the correct value of Vo.
TABLE-US-00009 TABLE 9 HB circuits from 4 coils, w/relative signal
amplitudes and root moments Relative Signal Moments (Hz) Coils
Amplitude 1st Root-2nd Root-3rd N1oS1 2.83 636.1 684.2 1224.3 N1oN2
1.15 843.0 752.3 1387.5 N1oS2 2.05 713.5 722.7 1295.3 S1oN2 2.31
770.5 740.1 1337.7 S1oS2 0.88 835.0 752.8 1380.1 N2oS2 2.59 907.5
771.0 1440.7 N1oS1N2 0.78 933.1 794.6 1474.9 N1oN2S2 0.23 1201.1
873.1 1724.2 N1oS1S2 2.59 669.8 717.1 1275.0 S1oN1S2 1.91 655.1
704.8 1252.0 S1oN2S2 1.33 637.4 687.4 1226.4 S1oN1N2 2.23 672.2
704.6 1259.0 N2oN1S1 0.31 849.3 824.7 1468.2 N2oN1S2 0.74 712.6
718.1 1288.1 N2oS1S2 2.18 792.8 752.8 1363.7 S2oN1S1 0.36 837.2
822.7 1454.7 S2oN2S1 1.30 683.4 714.9 1274.3 S2oN1N2 2.64 792.9
754.2 1362.3 N1oS1N2S2 0.40 633.2 708.9 1247.4 S1oN1N2S2 0.63 632.9
699.4 1235.3 N2oN1S1S2 0.26 854.7 756.4 1398.3 S2oN1S1N2 0.49 827.6
783.5 1413.4 N1N2oS1S2 2.55 741.4 743.2 1329.1 N1S2oS1N2 1.02 837.0
750.1 1379.9 N1S1oN2S2 0.25 1006.8 868.2 1598.4
TABLE-US-00010 TABLE 10 25 results ordered by mean frequency from
low to high Relative Linear Signal Moments (Hz) Coils Amplitude 1st
Root-2nd Root-3rd S1oN1N2S2 0.63 632.9 699.4 1235.3 N1oS1N2S2 0.40
633.2 708.9 1247.4 N1oS1 2.83 636.1 684.2 1224.3 S1oN2S2 1.33 637.4
687.4 1226.4 S1oN1S2 1.91 655.1 704.8 1252.0 N1oS1S2 2.59 669.8
717.1 1275.0 S1oN1N2 2.23 672.2 704.6 1259.0 S2oN2S1 1.30 683.4
714.9 1274.3 N2oN1S2 0.74 712.6 718.1 1288.1 N1oS2 2.05 713.5 722.7
1295.3 N1N2oS1S2 2.55 741.4 743.2 1329.1 S1oN2 2.31 770.5 740.1
1337.7 N2oS1S2 2.18 792.8 752.8 1363.7 S2oN1N2 2.64 792.9 754.2
1362.3 S2oN1S1N2 0.49 827.6 783.5 1413.4 S1oS2 0.88 835.0 752.8
1380.1 N1S2oS1N2 1.02 837.0 750.1 1379.9 S2oN1S1 0.36 837.2 822.7
1454.7 N1oN2 1.15 843.0 752.3 1387.5 N2oN1S1 0.31 849.3 824.7
1468.2 N2oN1S1S2 0.26 854.7 756.4 1398.3 N2oS2 2.59 907.5 771.0
1440.7 N1oS1N2 0.78 933.1 794.6 1474.9 N1S1oN2S2 0.25 1006.8 868.2
1598.4 N1oN2S2 0.23 1201.1 873.1 1724.2
Table 10 shows the same results, ordered by the 1.sup.st moment,
which is the mean frequency of the spectral analysis, with a range
from 632.9 to 1201.1 Hz. FIG. 6 shows the same results for mean
frequency versus frequency order. It highlights the equivalent
3-way switch results, the neck humbucker (Neck HB) at the 3.sup.rd
spot, 636.1 Hz, the neck and bridge humbuckers in parallel
(Neck.parallel.Bridge) at the 11.sup.th spot, 741.4 Hz, and the
bridge humbucker (Bridge HB) at the 22.sup.nd spot, 907.5 Hz. It
shows a number of frequencies bunched closely together, at 632.9 to
639.4 Hz, 669.8 and 672.2 Hz, 712.6 and 713.5 Hz, 792.8 and 792.9
Hz, and from 835.0 to 837.2 Hz. Note that the four results above
854.7 Hz have a much steeper curve, and the top three have a lower
signal strength, and that the results in general tend to be bunched
at the low end, at the presumably warmer tones, and again in the
middle-high range between 800 and 900 Hz. Without having done the
measurements, one can only speculate that the distribution may have
be more even for four matched and evenly spaced pickups, as
described in U.S. Pat. No. 9,401,134 (Baker, 2016).
This suggests that there may be only 17 distinct tones available, a
result consistent with a two-humbucker experiment in NP patent
application Ser. No. 15/616,396 (Baker, 2017) using a 20-circuit
switch. Note also that the relative signal strengths run from 0.23
to 2.83, a factor of 12.3, or about 22 dB. This data will be used
to demonstrate a method for ordering tones and choosing switching
connections accordingly, with variable gains to equalize signal
strengths.
Embodiments of Electro-Mechanical Switching Systems
For 3 unmatched single-coil pickups, there are 47 different
series-parallel circuits. For 3 matched single-coil pickups, there
are 6 different humbucking series-parallel pairs, plus 3 humbucking
triples for a total of 9 different humbucking circuits. For 4
unmatched single-coil pickups, there are 620 different
series-parallel circuits. For 2 humbuckers with 4 matched coils,
there are 20 series-parallel arrangements, considering only the
internal humbucker series-parallel connections and the external
humbucker to humbucker series-parallel connections. For 4 matched
single-coil pickups, there are 48 combinations of humbucking pairs
and quads, with 12 humbucking triples and 4 humbucking circuits
with one pickup over three, for a total of 64 different humbucking
circuits. The humbucking circuits with 2 over 2 pickups duplicate
humbucking quads already constructed.
The simplicity of the circuits disclosed here, using the Four
Simple Rules, reduces the number of humbucking circuits from 9 to 6
for 3 matched pickups, and from 64 to 25 humbucking circuits for 4
matched single-coil pickups. This, in exchange for simplified
switching that can be ordered according to the warmth (or at least
the mean frequency) of humbucking tones. This switching system can
be achieved with a number of different embodiments, from those
using available mechanical switches, to those with both mechanical
switches and active amplifiers, to those with
microprocessor-controlled switching and gains. As the following
examples show, there are a wide number of possible embodiments, not
limited to just those depicted here.
Embodiment 1: 3 Matched Coils with a 4P6T Switch
In FIG. 7, as is common, dots at line crossings show connections
and crossing without dots are pass-overs, as with the lines above
C.sub.T1 and C.sub.T2. The pickups coils N1 and N2 are N-up, with
the negative terminals connected in common with the positive
terminal of S1, an S-up coil, at the common connection point (1).
Note that only 3 of the 4 poles are needed to make the connections.
Which follow the humbucking rule of having at least one coil
connected to each side of the output, high and low. The 4.sup.th
pole can either be used for tone capacitors to match the circuit
lumped inductance, as shown, or for gain control resistors, if the
switched output goes into an amplifier. Note the signals listed
below each throw (1 to 6), N1-N2, N2+S1, N1+S1, N2+(S1-N1)/2,
N1+(S1-N2)/2, and (N1+N2)/2+S1, respectively.
If each of the matched coils have inductance, L.sub.C, then the
first three throws have circuit with a lumped inductance of
2*L.sub.C, and the last three have a lumped inductance of
3*L.sub.C/2. Tone capacitors C.sub.T1 and C.sub.T2 can be used to
maintain the equal effect of the tone pot, P.sub.T, on tone. Since
resonance frequency is a function of the product of inductance and
capacitance, the products, 2*L.sub.C*C.sub.T1 and
3*L.sub.C*C.sub.T2/2 must be equal to achieve similar tone results,
implying that C.sub.T1=3*C.sub.T2/4. Both the tone circuit and the
volume pot, P.sub.V, lie across the output of the switching
circuit. The wiper of the volume pot is connected to the output,
Vo.
This is not the only possible selection of matched coils. They
could all be either all S-up or all N-up. In which case, all the
outputs would be humbucking but out-of-phase, or contra-phase.
Without amplification and signal equalization, the output signals
would be much weaker, but much brighter. A selection of matched
coils that has only one S-up, as shown here, and a selection that
has only one N-up will produce the same tones if the opposite poles
from each set occupy the same positions under the strings. In other
words, N-S-N is the same as S-N-S. In the case of N-S-N, the
physical positioning of the S-up pole under the strings will also
determine tone, with different sets of tones from S-N-N and
N-N-S.
If the pickup magnetic poles are reversed to change the tonal
character of the guitar, each pole change will affect both the
frequency and order of tones. The order of tones for the switch
wiring for one set of poles likely will not hold for another. So
there must be some way to change the wiring of the switching along
with changing the poles to at least keep an order of tone monotonic
from warm to bright. U.S. Pat. No. 9,401,134 (Baker, 2016)
disclosed such a device in FIG. 30, a plug-in board with
cross-points to be soldered with through-hole jumpers to set the
switch connections.
FIG. 8 shows such a device for this example. One S-up pickup, S1,
and two N-up pickups, N1 and N2, have their common connection point
(1) connected to jumper, J2, and their other terminals connected to
the 4P6T switch, SW2. All of the switch throw interconnections are
made off the switch, on a plug board (13), connected to the throws
and one pole by a plug connector (15). The plug connector is shown
as a fingerboard connector, but can be anything that fulfills the
same function. The figure is split to show throws 1, 2, 5 and 6,
but not 3 and 4. One pole and the six related throws of the switch
connect to components X1 to X6 on the plug board, which can be any
kind of printed circuit board, hard or flexible, or anything else
that fulfills the function. Components X1 to X6 and the associated
pole of SW2 are connected off the board to the output, Xn. These
components can be resistors for gain control, or capacitors for
tone control, or some other function.
The other three times 6 throws, connect through a line of
cross-point interconnects (17) to the high output terminal, Vo+,
and through another line of interconnects to the low output
terminal, Vo-. The vertical circuit lines over the interconnects
are on one side of the board and the horizontal lines on the other,
so that they do not connect, except through the interconnects. The
interconnects can be either non-plated-through holes for soldered
through jumpers, or standard computer board jumpers, or some other
type that fulfills the function. The white dots show no connection,
and the black dots show interconnections. The interconnections
shown produce output voltages of Vo=V.sub.N2+V.sub.S1,
Vo=V.sub.N1-V.sub.N2, Vo=(V.sub.N1+V.sub.N2)/2+V.sub.S1, and
Vo=V.sub.N1+(V.sub.S1-V.sub.N2)/2, for throws 1, 2, 5 and 6,
respectively. Any combination and order of humbucking pairs and
triples, including duplicates, is possible.
At the output, only one of jumpers J1 and J2 may be connected. If
J1 is connected, then the lower terminal of Vo- is grounded, and
the output is single-ended, as are most electric guitar circuits.
If J2 is connected, then the common pickup connection point is
grounded and the output, Vo, is differential. A differential output
requires either that a differential amplifier convert it to
single-ended, or that the output jack of the electric guitar is
stereo, and feeds through 2-conductor shielded cable to a guitar
amp with a differential input. A single-ended output has the
advantage of using circuits and connections already common to
electric guitars. A differential output has the advantage of
suppressing common-mode electrical noise from external sources,
possibly such as fluorescent lights, which put out much higher
frequencies of noise than 60 Hz motors.
FIG. 8 can be adapted to any electro-mechanical pickup switching
system. Baker, NP patent application Ser. No. 15/917,389, 2018
shows how there can be 2.sup.J-1 pole configurations for J number
of matched single-coil pickups with reversible poles, or 4 pole
configurations for 3 pickups, each having 6 possible pickup
circuits, and 8 configurations for 4 pickups, each having 25
possible pickup circuits, and 16 configurations for 5 pickups, each
having 90 possible pickup circuits. This switching system requires
a pole for each pickup, and currently the most practical and
affordable switches have six poles or less, and six throws or less.
For example, with 3 pickups, a 4P6T switch can have one pole
dedicated to a set of adjustment components, resistive or
capacitive or something else, and a 5P6T switch can have two poles
dedicated to adjustment components, say resistive for gain control
with active circuits and capacitive for tone control.
Embodiment 2: Four Matched Coils with a 4P6T Switch
In this case, for a selection of poles from neck to bridge of N1,
S1, N2 and S2, all 4 poles of the switch are taken by the terminals
of the coils that are not connected at the common connection point
(1). Compact 6P6T switches, capable of fitting neatly under a pick
guard, are considerably less common, as well as much more
expensive. FIG. 9 shows this circuit, wired from throw 1 to 6,
respectively with the pickup circuits and the mean frequencies from
Table 10: (1) N1+(S1+S2-N2)/3, 633.2 Hz; (2) N1+(S1+S2)/2, 669.8
Hz; (3) N1+S2, 713.5 Hz; (4) (N1+N2)/2+(S1+S2)/2, 741.5 Hz; (5)
N1+(S1-N2)/2, 933.1 Hz; and (6) (N1-S1)/2+(S2-N2)/2, 1006.8 Hz.
Note that for the pair in throw 3, N1+S2, the lumped inductance of
the circuit is 2*Lc, where Lc is the inductance of the coil of any
matched pickup. For a humbucking triple, the lump inductance is
3*Lc/2, for a humbucking quad of 1-over-3, the inductance is
4*Lc/3, and for a humbucking quad of 2-over-2, the inductance is
Lc. There are no poles left on the switch to make adjustments to
the tone capacitor, so a tone circuit, T1, T2, T3 and T4 has been
placed across each pickup. This might be comprised of a tone
capacitor and a small multi-turn pot, accessible through a hole in
the pick guard. Or it could be four separate capacitors connected
to the switch end of each pickup, with a single 4-gang tone pot
connected to each capacitor and the common connection point.
Note also that the plug board in FIG. 8 can also work here, but
without the adjustment components, X1 to X6. If the pickups have
reversible poles, a plug board would be advisable, since there can
be 8 pole configurations and up to 25 switching circuits and 116
tones to choose from.
Embodiment 3: 3 Matched Pickups w/ Preamp & Signal Volume
Compensation
FIG. 10 shows this embodiment, with pickups N1 and N2 N-up, and S1
S-up. The 4P6T switch, SW4, uses 3 poles in a switching system with
a common connection point (1) to connect the pickups by throws: (1)
N1 over N2, or N1-N2; (2) N2 over S1, or S1+N2; (3) N1 over S1, or
N1+S1, (4) N2 over N1&S1, or N2+(S1-N1)/2; (5) N1 over
S1&N2, or N1+(S1-N2)/2; and (6) N1&N2 over S1, or
(N1+N2)/2+S1, where the pickup designations also stand in for
signal voltages. The circuit uses the 4.sup.th pole to switch gain
resistors, RG1 to RG6 into a circuit using operational amplifier U1
as a single-ended preamp with a feedback resistor, R.sub.F. Math 9
shows the gains produced. The output of U1 feeds a volume pot,
P.sub.V, which goes to the output jack, Vo. The tone controls are
T1, T2 and T3 across each pickup, each comprised of a tone pot,
R.sub.Ti, and tone capacitor, C.sub.Ti. Note that the lower
terminal of the switching system is grounded to the output, so the
common connection point cannot be.
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times. ##EQU00009##
TABLE-US-00011 TABLE 11 Example gain resistors for Embodiment 3,
FIG. 10, with R.sub.F = 47 k and R.sub.G1 = 2.2M Throw 1 2 3 4 5 6
Relative 3.161 2.051 2.311 1.148 2.519 0.252 Amplitude Gi# = 1 1.54
1.37 2.75 1.25 12.54 Gi = 1.021 1.57 1.40 2.81 1.28 12.81 g*Gi# =
R.sub.Gi(k.OMEGA.) 2200 82 128 26 170 4
Since we have no experimental data for a 3-coil guitar, let the
relative signal amplitudes before amplification in Table 11 stand
in for the sake of argument and example. We conveniently choose the
maximum relative signal strength of 3.161 as the first gain, and we
wish to adjust the other gains to bring all the other signals up to
that level at the output, Vo. Dividing that relative amplitude by
all the others, give the relative gain, Gi#, for each signal that
we need to approach. But if we pick a feedback resistor, R.sub.F=47
k, and a minimum gain resistor R.sub.G1=2200 k, or 2.2M, then the
first gain will be 1.024 instead of 1. We have to multiply this
number times all the gains to get the real gains, then calculate
R.sub.Gi. Math 9 and Table 11 show these calculations.
Only a few of the R.sub.Gi values are close to standard resistor
values. Given that and the differences between human perception and
electronic measurements, it would be better to use small, square
multi-turn potentiometers for the other R.sub.Gi. And if any of the
pickup poles are to be reversed, it would be better to use a
connection plug board, like that in FIG. 8, with the pots mounted
in place of the components, Xi.
Embodiment 4: 3 Matched Coils w/4P6T Switch & Differential
Preamp
FIG. 11 show this embodiment. It differs from FIG. 10 by grounding
the common connection point (1) of the pickups, N1, S1 and N2, and
by having a preamp with a differential input and a single-ended
output. A differential amplifier has the advantage of removing
pickup signal common-mode voltages at the preamp input, Vs+ and
Vs-, from the output, Vo. So if the pickups see an external.
interference signal that raises all of their voltages at the SW5
switch poles above ground, it essentially disappears at Vo, reduced
by up to 100 decibels. The gain calculations are also different, as
shown in Math 10, being about twice as large as a single-ended
amplifier for the same values of R.sub.F and R.sub.G. Again, if one
intends to reverse any pickup poles, the plug board from FIG. 8
should be added to the circuit, and the components X1 to X6
replaced with R.sub.G1 to R.sub.G6, preferably small, multi-turn
pots.
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times. ##EQU00010##
Embodiment 5: 3 Humbuckers with 6PXT Switch
FIG. 12 shows this embodiment, simply as the humbuckers and the
poles of a 6-pole, multi-throw switch, merely to show how the
common connection point (1) works with dual-coil humbucking
pickups. The center taps, between the N-up and S-up, coils are all
connected together, and grounded according to Rule 3, depending on
whether the output terminals of the switch, SW6, are to be
single-ended (ungrounded) or differential (grounded). Since there
are a possible 301 combinations of humbucking pairs, triples, quad,
quints and hexes for the 6 coils of 3 humbuckers, and a $50.00 6P6T
switch is at the upper end of capability for available mechanical
switches, this illustrates the need for something better, namely
digitally-controlled analog switching.
Embodiment 6: 2 Humbuckers w/6P6T Switch and Differential
Preamp
FIG. 13 shows 2 humbuckers connected to 4 poles of a 6P6T switch,
SW7, using 6 of the circuit configurations of Table 10 as an
example, as shown in Table 12, going from the bright tone on throw
1 to the warm tone on throw 6. The connections have been inverted
from Table 10 in throws 4 & 6 to keep most of the signal signs
positive. The inductance of a single coil is L.sub.C. Note that the
center taps of the humbuckers are connected to a grounded common
connection point (1), as in FIG. 12.
TABLE-US-00012 TABLE 12 Order of tone mean frequencies from 1201 Hz
to 633 Hz for a 6P6T switch Lumped circuit Throw Pickup circuit
signal Mean freq (Hz) inductance 1 N1 + (S2 - N2)/2 1201.1
3*L.sub.c/2 2 (N1 - S1)/2 + (S2 - N2)/2 1006.8 L.sub.c 3 N1 + (S1 -
N2)/2 933.1 3*L.sub.c/2 4 (N1 + N2 - S1)/3 + S2 827.6 4*L.sub.c/3 5
N1 + S2 713.5 L.sub.c 6 (N1 + N2 - S2)/3 + S1 632.9 4*L.sub.c/3
Since only 4 poles of the 6 pole switch are needed to switch the
pickup terminals to the switch output, .DELTA.Vs, the other 2 are
available to switch the gain resistors, R.sub.Gi, and the tone
capacitors, C.sub.Ti. The gain resistors are again calculated
according to the principles of Math 10 and Table 11, according to
the measured relative signal amplitudes of .DELTA.Vs for all 6
throws. Since the resonant or low-pass frequency of an inductor and
capacitor goes according to the product of LC, Math 11 shows the
relationships between the values of C.sub.Ti, for which only 3
actual capacitors are needed, since there are only 3 lumped values
of switched circuit inductance.
.times..times..pi..times..times..times..times..times..times..times..times-
..times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times..times.
##EQU00011##
The tone circuit can be any useful form, such as Tone Circuit 1 or
Tone Circuit 2. The switch output, .DELTA.Vs, feeds into the
differential amplifier comprised of U1a, U1b, 2 feedback resistors,
R.sub.F, and the switched gain resistor, R.sub.Gi, has a
differential output, .DELTA.Vo. Considering that the four coils can
be connected into 25 different circuits with this switching system,
and with 116 potentially unique tones, using the plug board of FIG.
8 would make the system more versatile. Using the bottom two poles
and throws in FIG. 13, the plug board components, X1 to X6, could
be replaced by small pots for the R.sub.Gi, and doubled, adding a
capacitor, C.sub.Ti, and small pot, P.sub.Ti, each comprising Tone
Circuit 2 in the second set of components X7 to X12.
Embodiments of Analog-Digital Switching Systems
The possibility results of Tables 4, 6, 7 and 10, of so many more
configurations and tones than electro-mechanical switches can
control, justify the use of digitally-controlled analog switches.
Micro-power micro-controllers (uC) offer display, user interfaces,
control and longer battery life, but few if any have the arithmetic
processing units with the necessary trigonometric functions to
calculate Fast Fourier transforms, which might be used to order
tones. It will likely be necessary to add math processing units
(MPUs). With such capability, and not yet fully determined
algorithm for determining timbre and tone from strummed strings, it
should be possible to offer the musician a user interface with a
simple one-switch to one-swipe control to shift progressively from
bright to warm tones and back without the musician ever needed to
know which pickups are used in what configurations. In this
disclosure, the mean frequency of six strummed strings is used as
an example of the order of tone, which will likely be superseded by
other measures. Nevertheless, the system architecture that will
allow such measures and control will remain relatively constant for
a while.
Embodiment 7: J=K Coils w/ Digital Control of SMD Analog
Switches
Suppose that we have J number of N-up pickup coils and K number of
S-up pickup coils, and we have chosen to use the common connection
point switching system, where one terminal of each coil, regardless
of magnetic pole direction (or electric pole for other sensors),
are connected to a single point according to the same phase of
external hum. In this switching system, there are 3 choices, or 3
states, for the other terminals of each coil to be connected by the
switching circuit: 1) connected to the low output terminal of the
switching system; 2) connected to the high output terminal of the
switching system; or 3) not connected to either terminal. There is
also the choice of how the ground is connected in the switching
system, according to Rule 3. It is connected either to the low
output terminal, or to the pickup common connection point. It is
also possible to break the Rule, and ground both the common pickup
connection and the low output terminal, so as to isolate the output
of just one coil connected to the high output, for tuning and
measurement purposes.
For this we need digitally-controlled solid-state analog signal
switches to reach the full potential of a switching system with
more than 3 or 4 coils. FIG. 14 shows two such switches, a
single-pole double-throw switch (FIG. 14A), and a single-pole
triple throw switch (FIG. 14B), with the additional state of no
connection at all. The 1P2T switch in FIG. 14B has a normally
closed (NC) connection to the single pole, A, when the digital
control, S, is at a low or binary "0" state. When S=1, A is
connected to the normally open connection, NO. The 1P2T switch can
be used to connect the system analog ground to either the low
output terminal or to connect the low output terminal to the pickup
common connection, depending upon whether the amplifier at the
switching system output is single-ended or differential. Or it can
be used to switch tone capacitors.
The 1P3T switch in FIG. 14B, has one pole, A, which is connected as
shown in the table for the digital inputs, (S1, S0), to B0, B1, B2
or nothing, an open circuit, NO. When the digital state of
(S1,S0)=(0,0), the A terminal is connected to nothing, like an open
circuit. When (S1,S0)=(0,1), A is connected to B0, which can be the
low output terminal. When it is (S1,S0)=(1,0), A is connected to
B1, which can be the high output terminal. When (S1,S0)=(1,1), A is
connected to B2, which can be the pickup common connection, this
shorting out the coil. The best use of either (S1,S0)=(0,0) or
(1,1) remains to be determined, according to the best performance
of the circuit, but should have very similar results.
While it is possible to use a digitally controlled analog
cross-point switch, they can come as large DIP chips, with more
than a score of pins, or require supply voltages in excess of 5V,
or have contact resistances of tens of ohms. A cross-point switch
typically addresses only one contact at a time, requiring
addressing and data strobing for each separate connection. For a
6.times.8 cross-point switch (should one exist), used with four
coils, a set of gain resistors and a set of tone capacitors, there
are 6*8=48 different cross-connections that have to be set
individually by addressing.
The switches in FIG. 14 have only 1 or 2 bits of digital control,
which can be the output lines of a micro-controller. In some cases,
it may be advisable to add latches, if those uC lines are also used
for other functions. The switches are small surface mount devices,
often costing less than a dollar (US) each, with contact
resistances down to about 1 ohm.
With 4 coils, there are as may as 25 possible circuits requiring as
many as 25 gain resistors to equalize the signal voltages. Or,
alternatively and more efficiently, since a micro-controller is now
available, digital pots can be used to set gain. FIG. 15 shows a
single-ended amplifier (15A) and a differential amplifier (15B),
with feedback digital pots PF, P.sub.Fa and P.sub.Fb, op-amps U1,
U2a and U2b, and 2 gain resistors, R.sub.G. The digital feedback
pots can be 100 k with 256 equal steps. Math 12a&b show the
equations for the pots and circuit gain. The dotted line between
P.sub.Fa and P.sub.Fb indicates that they must be set to the same
wiper positions in tandem to keep the output balanced about signal
ground. Some digital pots come 2 to a chip. The output of the
differential amp can be either differential, as shown, for use in
further signal conditioning, or use the single-ended output
structure of U3, R.sub.F and P.sub.V in FIG. 11.
.times..times..times..times..times."".times..times..times..times..times..-
times..times..times..times..times..times..times..times..times..times..time-
s..times..times..times..times..times..times..times..times..times..times..t-
imes..times..times..times..times..times..times..times..times..times..times-
..times..times. ##EQU00012##
Calculations elsewhere, using the resistance granularity of digital
pots, indicate that using digital pots to set gain in FIG. 15a,
with 256 equal resistance steps, P.sub.F=100 k and R.sub.G=5.1 k,
can equalize the relative amplitudes in Tables 9 & 10 within a
range of .+-.5%, over a gain range of G=1.0 to 20.6. Digital pots
typically have a serial interface comprised of 3 lines. For 4
coils, there are only 3 different lumped circuit inductances. So
only 3 tone capacitors are needed to compensate for those
differences, possible with 3 of the 1P2T switches, requiring 3
lines of digital control, or 1 of the 1P3T switches, using 2 lines
of digital control. FIG. 16 shows these alternatives, the 1P2T
switches in FIG. 16A, and the single 1P3T switch in FIG. 16B,
driven directly by the digital I/O lines of a micro-controller. In
FIG. 16A, the tone pot, P.sub.T, is manual, and in FIG. 16B, it is
digital, P.sub.TD, with 3 control lines going to the uC I/O. Either
pot could be used in either side, depending on the overall circuit
design. The circuit in 16A can produce 7 possible tone
capacitances, or none, by connecting 0, 1, 2 or 3 in parallel. The
circuit in 16B can produce only 3. Table 13 shows the number of uC
input/output lines needed for 4 coils, according to the circuits in
FIGS. 14-17. It may be advisable to use addressing and latches if
some of these lines are to be used for other functions, such as
User Controls and Displays.
TABLE-US-00013 TABLE 13 Numbers of uC I/O lines needed for 4 coils
in FIG. 17 min max 4 coils 4 1P3T 4 1P3T 8 8 3 tone caps 1 1P3T 3
1P2T 2 3 Tone pot manual digital 0 3 Single-ended or diff amp 1 dig
pot 2 dig pots 3 6 Volume pot manual digital 0 3 Total 13 23
FIG. 17 shows a micro-controller architecture for switching the
combinations of J number of N-up coils, N1 to Nj, with their
negative phase terminals connected to the common connection point
(1), also denoted by a "C" in a triangle, and K number of S-up
coils, S1 to Sk, to the switching system output, Vs, and then on to
the analog signal conditioning circuits and the guitar output, Vo.
The intermediate coils are not shown. The User Cntls & Display
and MPU sections are explained below, and the Analog Circuits
section is made up of circuits from FIGS. 10, 11, 15 and/or 16.
The outputs of the coils are switched by the respective 1P3T
digital-analog switches, SW1 to SWj, and SWj+1 to SWj+k. The
intermediate switches are not shown. The 1P3T switches, as in FIG.
14B, have a four-state output, leaving the A terminal normally
open, or connected to the B0 terminal, or the B1 terminal, or the
B2 terminals, which are shown reversed vertically from FIG. 14B, to
simplify the circuit. All the B0 switch terminals go to the high
switch output terminal, Vs+; all of the B1 switch terminals go to
the low switch output terminal, Vs-; and all of the B2 switch
terminals go to the pickup common terminal, triangle-C. So for each
of the (S1,S0) states, (S1,S0)=(0,0) disconnects the coil from any
other part of the circuit; (S1,S0)=(0,1) connects the coil to Vs+;
(S1,S0)=(1,0) connects the coil to Vs-; and; (S1,S0)=(1,1) connects
the coil to the common terminal, shorting it out. Whether shorting
the coil out has any effect on the tonal outputs remains to be
determined.
The two 1P2T switches, SWa and SWb, perform other functions. For
S=0, SWa connects the ground to the pickup common connections,
making the switching output, Vs+, suitable for connection to a
differential amplifier in the Analog Circuits section (FIGS. 10,
11, 13, 15&16, with FIG. 10 P.sub.V output for FIG. 15A and
FIG. 11 output for FIG. 15B). For S=1, SWa connects the ground to
Vs-, making Vs suitable for connection to a single-ended amplifier
in the Analog Circuits section. Since the Analog Circuits section
is not likely to be switchable between single-ended or differential
amplifiers, SWa could be replaced by a set of jumpers performing
the same function.
For S=0 (a separate control line from SWa), SWb shorts itself out
and has no function, but for S=1, it connects Vs- to the pickup
common connection point (1), allowing the output of a single pickup
coil, or a set of parallel pickup coils, connected to Vs+ to be fed
to the Analog Circuits section. This will be useful for measuring
or tuning single coils. The Analog Circuits section is taken to
contain all the analog signal circuits. FIG. 17 shows sensor and
control lines between it and the micro-controller, uC, to handle
such functions as the switching of tone capacitors.
The micro-controller, uC, is shown with two-way digital connections
to the User Controls and Display (adequately defined in NP patent
application Ser. No. 15/616,396); one-way control connections to
1P3T switches SW1 to SWj+k; one-way control connections to SWa and
SWb; one-way connections from the switching system output, Vs, to
an internal analog-to-digital converter (A/D); two-way sense and
control connections with the Analog Circuits section, and a Math
Processor Unit (MPU). The MPU section can be either internal to the
uC, if available, or an add-on co-processor. Either way must be
capable of at least 32-bit floating point operations on complex
variables, having sufficient trig and other math functions to
accomplish Fast Fourier Transforms (FFTs).
Using start-stop signals from the Analog Section or the User
Controls and Display, the FFT section performs complex FFTs on such
inputs as the six strummed strings, as described in "An experiment
with 2 mini-humbuckers". The FFT section takes A/D information from
the audio signal, Vs, to generate the complex FFTs needed for Math
8. The complex FFTs generated should have a resolution of at least
1 Hz, and a frequency range of at least 0 to 4 kHz, preferably to
10 kHz, and adjustable in bandwidth. It will be necessary to switch
the pickups during the A/D signal collection to obtain nearly
simultaneous sequential measurements either of all the coils
separately, and/or all the coils in humbucking pairs, corrected for
time delays according to Math 13, to produce effectively
simultaneous complex FFT spectra for the calculations in Math 8.
x(t-t.sub.0).revreaction.X(f)*e.sup.-j2.pi.ft.sup.0,e.sup.-j2.pi.ft.sup.0-
=cos(2.pi.ft.sub.0)-j sin(2.pi.t.sub.0) Math 13.
A digital-to-analog converter (D/A), which can be either internal
in the uC, or an external circuit, feeds the audio from inverse-FFT
transformations of measured signal spectra into the Analog Circuits
section to help the user recall pickup circuit tones and to make
better decisions on any user-defined tone switching sequences. From
this information, the switched coil combinations can be ordered by
mean output frequency from bright to warm or warm to bright, as a
first approximation of the order of tones. Or set by user
preference. The tones in signal output from the switching system
can be equalized in volume, according to Math 12ab, and Math 9 or
Math 11, in the Analog Circuits section by variable gains set by
the uC. Then the user can use the User Controls and Display to
shift monotonically from tone to tone without having to specify the
particular switched coil combination that produces it.
Embodiment 8: Digital Switching without a Micro-Controller
If for some reason a uC will not be used, the switching circuit in
FIG. 17 can be controlled by a simple up-down switch and an up-down
digital ripple counter using the same number of ripple outputs as
the number of desired circuits to be switched. The same 1P3T
solid-state switches can be used. Gain resistors and tone
capacitors can be switched from the same ripple counter control
signals. Another up-down switch and ripple counter can be used for
switching tone capacitors, if desired. Here again, the plug board
from FIG. 8 can be useful, especially if more than 3 pickups or
reversible-pole pickups are used. It can also be adapted to many
more than just 6 switched selections.
The single bit of each ripple output can be connected to multiple
switch control lines (S, S0 and S1 in FIG. 17), with each
connection set isolated from every other by something as simple as
diode or transistor isolators. Some digital signal inverters will
likely be necessary. In diode isolators, two or more diodes can be
connected with all the anodes, or all the cathodes connected to the
control line output from the ripple counter, and the other terminal
to each of the relevant switch controls. The direction of the diode
polarities depends only on whether the switch control lines have
either pull-up resistors to be pulled down by the ripple output, or
pull-down resistors to be pulled up. Schottky with a low forward
voltage drops will work best. It's an old technique dating back to
the diode-transistor logic (DTL) of the 1960s that still works.
It's so old and simple that a Figure is not necessary to illustrate
it.
Method of Choosing the Spacing and Switching Order of Tones
The object of the exercise is to offer a much wider range of tones,
and to allow the musician to use one control to shift progressively
from bright to warm and back, without ever needing to know which
pickups are used in what circuit. For that, one needs a way to
order the tones.
There is no guarantee at this time that using the mean frequency of
the signal from one or more strummed strings, with either open
fretting or some chord, will correspond exactly to brightness or
warmness of tone, as commonly perceived by a musician's ears. For
example, R. M. French (2009, Engineering the Guitar, Theory and
Practice, Springer, N.Y.) noted in a section on psychoacoustics, pp
190-193, that louder tones mask nearby tones. And on pp 29-36, in a
section on human perception of sound, he notes that the sensitivity
of human hearing to tones peaks at 1000 to 2000 Hz. This method of
ordering tones needs a simple one-number measure of tone that has
not yet been developed and proven. But the mean frequency of six
strummed strings is a start, used here as an example until better
methods come along.
The mean-frequency numbers used here for illustrating the method
come from Math 8 and Table 10, from the dual-humbucker experiment
previously disclosed, which also helps to illustrate the method.
Ideally, the frequency resolution should be 1 Hz, with a range of
from 0 Hz to a top end of at least 4 kHz, but preferably the full
range of human hearing, which extends to 20 kHz or more.
Preferably, enough sample windows should be taken to cover from the
very beginning of a strummed or plucked note or chord through the
full sustain of the sound. But it may turn out that other sampling
techniques have certain advantages not discussed here.
One should expect that, like the dual-humbucker experiment, some
tones will be too close together to count, and the separation of
tones with switched pickups circuits will vary considerably, likely
with most of the tones bunched together at the warm end. So, for
four pickups with 25 different circuits, there may be only half
that number of useful tones. And for 25 different circuits and a
six throw switch, only half of those can be used. For pickups with
reversible poles, four pickups have 8 different pole
configurations, sharing 25-member sets of 116 potentially unique
tones. (The ratio of the numbers poles times circuits to the
numbers of tones is always greater than or equal to one.)
Digitally-controlled analog switching may have a much wider range
of choice than mechanical switches, but the problem of bunched
tones still exists. Note that in Table 10, the range of mean
frequency from 632.9 Hz at the low end to 1201.1 Hz at the high
end, for one pole configuration, is barely an octave. Without
actual measurements, it is not yet possible to know what other pole
configurations will produce. Nor is it yet possible to account for
the variations introduced by moving pickups themselves about in
space, as disclosed in U.S. Pat. No. 9,401,134B2 (Baker, 2016),
offering 5 degrees of freedom, vertically and along the strings at
each end of a pickup, as well as across the strings.
This method assumes that whatever the measure of tone, it should be
divided along bright to warm, or warm to bright, according to
virtual frets. In most Western music, adjacent notes differ by a
multiplier or divisor of 2.sup.1/12, counting 0 to 12 frets from an
open note to its octave note. Other musical traditions can have
three times as many notes in an octave. This division of
frequencies comes from the way that the human ear is constructed
and responds to sound. So it is natural to assume that the most
effective and efficient way to chose the separation of tones chosen
and ordered from those available is by a constant frequency
multiplier from one tone to the next higher tone.
The method disclosed here is fairly simple: (1) chose a measure of
tone (mean frequency of six strummed strings from FFT analysis in
these examples); (2) cause the musical instrument to emit tones in
some standard fashion (strum six strings several times in these
examples); (3a) take digital acoustic samples of the signal outputs
from each pickup simultaneously (not quite possible in these
examples), or alternatively, (3b) take digital acoustic samples
from each switched pickup circuit; (4) digitally process the
acoustic samples to obtain complex number frequency spectra for
each pickup or each pickup circuit (only magnitudes of frequency
bins were possible for these examples, leaving out phase
information); (5) apply the measure of tone to the individual
frequency spectra (Math 8 and Table 10 in these examples); (6) pick
the range of tones (from mean frequencies in Table 10 in these
examples); (7) pick the number of tones to be switched (for
example, six tones for a 6 throw switch); (8) calculate the virtual
fret steps between switched tones; (9) choose the closest available
tones to those steps; and (10) wire or program the mechanical and
digital-analog switch to select the circuits that produce those
tones.
Since human hearing is very subjective, there's an alternative
extension to the method that orders the tones according to the
musician's preference. Anytime after step 4, when the samples have
been taken and FFT transforms have been stored, the inverse-FFT
transform can convert the spectra back into a string of sounds. The
sound that comes out will be the average of all the sample windows
taken over the entire original length of the notes. So the strike
and decay of the sound may be averaged together.
It's the Optometrist approach, and requires either the use of a
micro-controller with a digital-to-analog converter to produce the
sounds and ask the musician for decisions, or presentation by a
person customizing the guitar. The inverse-FFT characteristic sound
of each of two switched circuits plays back to the musician, and
the software asks, "Which sound is warmer? Tone A? Or Tone B?" Or,
the guitar customizer simply plays the tones on the guitar and asks
the same questions. Then the musician picks, and the use of an
efficient sorting algorithm, such as a shell sort, determines the
order of the tones for switching. Then the entire set is played
back in order for confirmation and adjustment.
The following examples include equations and tables to help
illustrate the method.
Example 1: Choosing 6 Tones from Table 10 Using Mean Frequency for
a 6P6T Switch
Suppose that the only switch available is a 6P6T mechanical switch,
and we wish to use the entire frequency range in Table 10 from
632.9 to 1201.1 Hz. Math 14 shows a simple way to calculate the
ratio between frequency steps, r, where the lowest frequency, 632.9
Hz, is multiplied by r five times to get the highest frequency and
all the steps in between for a 6-throw switch.
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mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..function..function..times..times..times..times..time-
s..times..times..times..function..times..times..times.
##EQU00013##
It is usually not possible to use the measured mean frequencies to
hit those marks exactly. So one takes the choices that seem best.
The first frequency, 632.9 Hz, has a pickup combination,
S1overN1N2S2, a quad circuit. The closest ones to 719.4 Hz are
712.6 at 0.74 relative amplitude and 713.5 at 2.05 amplitude. The
best choice is 713.5 Hz, from combination N1overS2. The 3.sup.rd
frequency, 817.8 Hz, is 24.9 Hz up from 792.9 and 9.8 Hz down from
827.0 Hz. If signal strength is important, then the lower frequency
would be better, but the relative amplitude of the highest
frequency output, 1201.1 Hz only has a relative amplitude of 0.23,
so S2overN1S1N2 at 827.0 Hz it is. The closest and only choices for
929.6 and 1056.6 Hz are N1overS1N2 at 933.1 Hz and N1S1over N2S2 at
1006.8 Hz, leaving N1overN2S2 at 1201.1 Hz. Table 14 shows the
chosen order brightest to warmest tones, according to the mean
frequencies of 6 strummed strings.
TABLE-US-00014 TABLE 14 Order of tones from 1202 Hz to 633 Hz for a
6P6T switch Throw 1 2 3 4 5 6 Pickup N1 N1S1 N1 S2 N1 S1 circuit
N2S2 N2S2 S1N2 N1S1N2 S2 N1N2S2 Mean freq 1201.1 1006.8 933.1 827.6
713.5 632.9 (Hz) ~Fret 11.1 8.0 6.7 4.6 2.1 0 number Relative 0.23
0.25 0.78 0.49 2.05 0.63 Amplitude
Compare this to Table 15, representing a 3-way switch giving the
bridge HB, the neck and bridge HB in parallel, and the neck HB.
TABLE-US-00015 TABLE 15 Outputs for a standard 3-way switch Throw 1
2 3 Pickup circuit N2 N1N2 N1 S2 S1S2 S1 Mean freq (Hz) 907.5 741.4
636.1 ~Fret number 6.2 2.7 0 Relative Amplitude 2.59 2.55 2.83
The representation for the middle of the 3-way switch may not be
entirely correct, because in this circuit, the center taps of the
HB are connected to each other, whereas they are not with a
standard 3-way switch. Note also that the relative amplitudes for
choices on the 3-way switch are relatively equal to each other, and
much larger than those for this switching system using a 6-way
switch, by as much as 12.3 times. This means that the output of the
6P6T switching system will have to be electronically amplified, and
the gains switched as well to equalize the volumes of the signals.
This was addressed in the section on embodiments.
Example 2: Choosing 6 Tones from Table 4 Using Weighted Moments
Suppose it should be determined that a better measure of tones
comes from giving a weight of 1 to the mean frequency, 1/2 to the
square root of the 2.sup.nd moment, and 1/3 to the 3.sup.rd root of
the 3rd moment in Table 3. The normalized fractions would be 6/11
of the mean frequency, 3/11 of the root 2.sup.nd moment and 2/11 of
the root 3.sup.rd moment, as shown ordered by Weighted moments in
Table 16.
TABLE-US-00016 TABLE 16 Coil circuits ordered by weighted moments,
Weighted = 6*(1.sup.st)/11 + 3*(root-2.sup.nd)/11 +
2*(root-3.sup.rd)/11 Signal Moments (Hz) Coils Amplitude 1st
Root-2nd Root-3rd Weighted N1oS1 2.83 636.1 684.2 1224.3 756.2
S1oN2S2 1.33 637.4 687.4 1226.4 758.1 S1oN1N2S2 0.63 632.9 699.4
1235.3 760.6 N1oS1N2S2 0.40 633.2 708.9 1247.4 765.5 S1oN1S2 1.91
655.1 704.8 1252.0 777.2 S1oN1N2 2.23 672.2 704.6 1259.0 787.7
N1oS1S2 2.59 669.8 717.1 1275.0 792.7 S2oN2S1 1.30 683.4 714.9
1274.3 799.4 N2oN1S2 0.74 712.6 718.1 1288.1 818.7 N1oS2 2.05 713.5
722.7 1295.3 821.8 N1N2oS1S2 2.55 741.4 743.2 1329.1 848.7 S1oN2
2.31 770.5 740.1 1337.7 865.3 N2oS1S2 2.18 792.8 752.8 1363.7 885.7
S2oN1N2 2.64 792.9 754.2 1362.3 885.8 S1oS2 0.88 835.0 752.8 1380.1
911.7 N1S2oS1N2 1.02 837.0 750.1 1379.9 912.0 N1oN2 1.15 843.0
752.3 1387.5 917.3 S2oN1S1N2 0.49 827.6 783.5 1413.4 922.1
N2oN1S1S2 0.26 854.7 756.4 1398.3 926.7 S2oN1S1 0.36 837.2 822.7
1454.7 945.5 N2oN1S1 0.31 849.3 824.7 1468.2 955.1 N2oS2 2.59 907.5
771.0 1440.7 967.2 N1oS1N2 0.78 933.1 794.6 1474.9 993.8 N1S1oN2S2
0.25 1006.8 868.2 1598.4 1076.5 N1oN2S2 0.23 1201.1 873.1 1724.2
1206.7
Suppose that the same 6-throw switch will be used, with 756.2 Hz
the lowest tone, 1206.7 Hz the highest tone, and 4 in between, all
separated by the same frequency multiplier. Math 15 shows the
calculations.
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mes..times..times..times..times..times..times..times..times..times..times.-
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s..times..times..times..function..times..times..times.
##EQU00014##
For 830.3 Hz, 821.8 is 8.5 Hz below and 848.7 is 18.4 above,
leaving 821.8 Hz the closest. For 911.6 Hz, 911.7 is closest. For
1001.0 Hz 993.8 Hz is closest, leaving 1076.5 for 1099.0 and 1206.7
Hz. Table 7 shows the results of these choices. Because of the
dearth of choices at the high end, only the choices for throws 4
and 6 have changed from Table 4.
TABLE-US-00017 TABLE 17 Order of 6 tones from 1207 Hz to 756 Hz for
Weighted moments Throw 1 2 3 4 5 6 Pickup N1 N1S1 N1 S1 N1 N1
circuit N2S2 N2S2 S1N2 S2 S2 S1 Mean freq 1206.7 1076.5 993.8 911.7
821.8 756.2 (Hz) ~Fret 8.1 6.1 4.7 3.2 1.4 0 number Relative 0.23
0.25 0.78 0.88 2.05 2.83 Amplitude
Example 3: Steps of 1/2 Fret or More from Table 3 Using Mean
Frequency
Suppose that we wish to remove the near-duplicate tones by
specifying that the difference in virtual fret step between tones
be 0.5 fret or greater, or a frequency multiplier of 2.sup.1/24,
from Table 10. Obviously, not all of those slots will be filled,
and some closer choice may be sacrificed for another with a larger
signal. Table 18 shows the first-cut list, choosing 12 out of 25
circuits, with approximate fret steps between mean-frequency
choices ranging from 0.5 to 3.1. The first column starts with the
first choice, 632.9 Hz, with the value for the half-fret step up in
the second column. The next value in the first column is taken from
that, either 0.5 fret or more, and so on, except that 933.1 Hz is
chosen instead of 934.1 Hz because it is so close. The signal for
792.9 Hz was chosen over 792.8 Hz because it had a stronger signal.
The 3.sup.rd column shows the relative number of frets from 632.9
Hz; the 4.sup.th shows the relative measured amplitude of the
signal derived from 6 strummed strings; and the 5.sup.th shows the
coil connections, with the "+" output shown over the "-" output.
The 6.sup.th column shows the amplifier gain for each switching
combination required to equalize all the signals to the amplitude
of the strongest signal, 792.9 Hz for S2 over N1N2. They range from
1.0 to 11.47
TABLE-US-00018 TABLE 18 Half-fret or more steps from Table 13
1/2-Fret Fret Relative Required Choice Up Step Amplitude Coils Gain
632.9 651.4 0.0 0.633 S1 4.17 N1N2S2 655.1 674.3 0.6 1.907 S1 1.38
N1S2 683.4 703.4 1.3 1.297 S2 2.03 N2S1 712.6 733.5 2.1 0.745 N2
3.54 N1S2 741.4 763.1 2.7 2.548 N1N2 1.03 S1S2 792.9 816.1 3.9
2.637 S2 1.00 N1N2 827.6 851.9 4.6 0.489 S2 5.40 N1S1N2 854.7 879.7
5.2 0.261 N2 10.10 N1S1S2 907.5 934.1 6.2 2.588 N2 1.02 S2 933.1
960.4 6.7 0.775 N1 3.40 S1N2 1006.8 1036.3 8.0 0.252 N1S1 10.46
N2S2 1201.1 1236.3 11.1 0.230 N1 11.47 N2S2
Example 4: Steps of 1/2 Fret or More from Table 6 Using Weighted
Moments
Table 19 shows the same method used for Table 18, using weighted
moments in Table 6, i.e.,
[6*(mean-freq)/11+3*(root-2.sup.nd)/11+2*(root-3.sup.rd)/11] (Hz).
In this table, 967.2 Hz with a 0.4 fret step is used because there
was nothing else closer, and it allowed 12 tones instead of just
11. This gives a range of fret steps between weighted moments of
0.4 to 2.0. Under the criterion of 0.5 fret step or more, it could
be discarded, leaving 11 tones, and a range of fret steps of 0.5 to
2.0. The range of gains required to equalize amplitudes goes from
1.0 to 12.32.
TABLE-US-00019 TABLE 19 Half-fret or more steps from Table 16 using
weighted moments 1/2 Fret Fret Relative Required Choice Up Step
Amplitude Coils Gain 756.2 778.3 0.0 2.83 N1 1.00 S1 777.2 800.0
0.5 1.91 S1 1.49 N1S2 799.4 822.8 1.0 1.30 S2 2.18 N2S1 821.8 845.9
1.4 2.05 N1 1.38 S2 848.7 873.6 2.0 2.55 N1N2 1.11 S1S2 885.8 911.8
2.7 2.64 S2 1.07 N1N2 911.7 938.4 3.2 0.88 S1 3.22 S2 945.5 973.2
3.9 0.36 S2 7.86 N1S1 967.2 995.6 4.3 2.59 N2 1.09 S2 993.8 1023.0
4.7 0.78 N1 3.65 S1N2 1076.5 1108.1 6.1 0.25 N1S1 11.24 N2S2 1206.7
8.1 0.23 N1 12.32 N2S2
* * * * *
References